Deck 9: Analytic Geometry

Question 1

Match the equation to its graph.

- $$x ^ { 2 } = - 12 y$$

A)


B)


C)


D)

Answer 1

Question 2

Graph the equation.

- $x^{2}=12 y$

A)


B)

C)


D)

Answer 2

Question 3

Graph the equation.

- $y^{2}=16 x$

A)


B)

C)


D)

Answer 3

Question 4

Match the equation to its graph.

- $$y ^ { 2 } = - 10 x$$

A)


B)


C)


D)

Question 5

Find an equation of the parabola described.

-Focus at (0, 21); directrix the line y = -21

A) $x ^ { 2 } = 84 y$
B) $y ^ { 2 } = 84 x$
C) $y ^ { 2 } = 21 x$
D) $x ^ { 2 } = - 84 y$

Question 6

Find the vertex, focus, and directrix of the parabola.

- $x^{2}=-8 y$

A) vertex: $( 0,0 )$
focus: $( 0,2 )$
directrix: $y = - 2$


B) vertex: $( 0,0 )$
focus: $( - 2,0 )$
directrix: $x = 2$


C) vertex: $( 0,0 )$
focus: $( 0 , - 2 )$
directrix: $y = 2$



D) vertex: $( 0,0 )$
focus: $( 2,0 )$
directrix: $x = - 2$

Question 7

Match the equation to its graph.

- $$y ^ { 2 } = 13 x$$

A)


B)


C)


D)

Question 8

Find an equation of the parabola described.

-Focus at (5, 0); vertex at (0, 0)

A) $y = 20 x ^ { 2 }$
B) $x = 20 y ^ { 2 }$
C) $x ^ { 2 } = 20 y$
D) $y ^ { 2 } = 20 x$

Question 9

Find an equation of the parabola described.

-Directrix the line y = 3; vertex at (0, 0)

A) $y = - \frac { 1 } { 12 } x ^ { 2 }$
B) $y = - 12 x ^ { 2 }$
C) $x = 3 y ^ { 2 }$
D) $x = - \frac { 1 } { 12 } y ^ { 2 }$

Question 10

Find an equation of the parabola described.

-Focus at (-3, 0); directrix the line x = 3

A) $y ^ { 2 } = - 12 x$
B) $x ^ { 2 } = - 12 y$
C) $y ^ { 2 } = - 3 x$
D) $y ^ { 2 } = 12 x$

Question 11

Name the conic.

A) circle
B) hyperbola
C) ellipse
D) parabola

Question 12

Name the conic.

A) circle
B) ellipse
C) hyperbola
D) parabola

Question 13

Match the equation to its graph.

- $x ^ { 2 } = 7 y$

A)


B)


C)


D)

Question 14

Find an equation of the parabola described.

-Focus at $( 4,0 ) ;$ vertex at $( 0,0 )$

A) $y ^ { 2 } = 16 x$
B) $x ^ { 2 } = 16 y$
C) $x ^ { 2 } = 4 y$
D) $y ^ { 2 } = 4 x$

Question 15

Name the conic.

A) circle
B) parabola
C) hyperbola
D) ellipse

Question 16

Find an equation of the parabola described.

-Vertex at (0, 0); axis of symmetry the x-axis; containing the point (9, 5)

A) $y ^ { 2 } = \frac { 25 } { 36 } x$
B) $y ^ { 2 } = \frac { 25 } { 9 } x$
C) $x ^ { 2 } = \frac { 25 } { 36 } y$
D) $x ^ { 2 } = \frac { 25 } { 9 } y$

Question 17

Name the conic.

A) parabola
B) circle
C) hyperbola
D) ellipse

Question 18

Find an equation of the parabola described and state the two points that define the latus rectum.

-Focus at (0, 4); directrix the line y = -4

A) $y ^ { 2 } = 4 x$ ; latus rectum: $( 9,2 )$ and $( - 9,2 )$
B) $x ^ { 2 } = 4 y$ ; latus rectum: $( 2,4 )$ and $( - 2,4 )$
C) $x ^ { 2 } = 16 y$ ; latus rectum: $( 8,4 )$ and $( - 8,4 )$
D) $x ^ { 2 } = 16 y$ ; latus rectum: $( 4,8 )$ and $( - 4,8 )$

Question 19

Graph the equation.

- $y^{2}=-20 x$

A)


B)

C)



D)

Question 20

Find the vertex, focus, and directrix of the parabola.

- $y^{2}=-12 x$

A)
$\begin{array}{l}\text { vertex: }(0,0) \\\text { focus: }(-3,0) \\\text { directrix: } x=3\end{array}$



B)
$\begin{array}{l}\text { vertex: }(0,0) \\\text { focus: }(3,0) \\\text { directrix: } x=-3\end{array}$

C) vertex: $( 0,0 )$
focus: $( 0 , - 3 )$
directrix: $y = 3$
11ed81f4_181c_1451_a8e7_855e330b9a6b_TB7697_11

D) vertex: $( 0,0 )$
focus: $( 0 , - 3 )$
directrix: $y = 3$

Question 21

Match the equation to the graph.

-

A) $x ^ { 2 } = 4 y$
B) $x ^ { 2 } = - 4 y$
C) $y ^ { 2 } = 4 x$
D) $y ^ { 2 } = - 4 x$

Question 22

Write an equation for the parabola.

-

A) $y ^ { 2 } = 8 x$
B) $x ^ { 2 } = - 8 y$
C) $x ^ { 2 } = 8 y$
D) $y ^ { 2 } = - 8 x$

Question 23

Graph the equation.

- $(y+1)^{2}=8(x-1)$

A)


B)


C)


D)

Question 24

Match the equation to the graph.

- $$( y + 2 ) ^ { 2 } = - 7 ( x - 1 )$$

A)


B)


C)


D)

Question 25

Find the vertex, focus, and directrix of the parabola. Graph the equation.

- $(x-3)^{2}=(y-3)$

A)
$\begin{array}{l}\text { vertex: }(3,3) \\\text { focus: }(3,3.25) \\\text { directrix: } y=2.75\end{array}$


B)
$\begin{array}{l}\text { vertex: }(-3,-3) \\\text { focus: }(-2.75,-3) \\\text { directrix: } x=-3.25\end{array}$


C)
$\begin{array}{l}\text { vertex: }(3,3) \\\text { focus: }(3.25,3) \\\text { directrix: } x=2.75\end{array}$



D)
vertex: $(-3,-3)$
focus: $(-3,-2.75)$
directrix: $y=-3.25$

Question 26

Find the vertex, focus, and directrix of the parabola. Graph the equation.

- $x^{2}-8 x=12 y-76$

A)
vertex: $(4,5)$
focus: $(4,2)$
directrix: $y=8$


B)
vertex: $(4,5)$
focus: $(7,5)$
directrix: $x=1$


C)
vertex: $(4,5)$
focus: $(1,5)$
directrix: $x=7$


D)
vertex: $(4,5)$
focus: $(4,8)$
directrix: $y=2$

Question 27

Find the vertex, focus, and directrix of the parabola. Graph the equation.

- $y^{2}+12 y=4 x-16$

A) vertex: $( - 5 , - 6 )$
focus: $( - 4 , - 6 )$
directrix: $x = - 6$


B) vertex: $( - 5 , - 6 )$
focus: $( - 6 , - 6 )$
directrix: $x = - 4$



C) vertex: $( - 5 , - 6 )$
focus: $( - 5 , - 7 )$
directrix: $y = - 5$


D) vertex: $( - 5 , - 6 )$
focus: $( - 5 , - 5 )$
directrix: $y = - 7$

Question 28

Match the equation to the graph.

- $$( x - 2 ) ^ { 2 } = 7 ( y - 1 )$$

A)



B)


C)


D)

Question 29

Find the vertex, focus, and directrix of the parabola with the given equation.

- $$( x + 1 ) ^ { 2 } = 12 ( y - 4 )$$

A) vertex: $( 1 , - 4 )$
focus: $( 1 , - 1 )$
$\text { directrix: } y=-7$

B) vertex: $( 4 , - 1 )$
focus: $( 4,2 )$
$\text { directrix: } y=-7$

C) vertex: $( - 1,4 )$
focus: $( - 1,1 )$
$\text { directrix: } y=-7$

D) vertex: $( - 1,4 )$
focus: $( - 1,7 )$
$\text { directrix: } y=-7$

Question 30

Find an equation for the parabola described.

-Vertex at (6, 1); focus at (6, 3)

A) $( y - 1 ) ^ { 2 } = - 12 ( x - 6 )$
B) $( y - 1 ) ^ { 2 } = 12 ( x - 6 )$
C) $( x - 6 ) ^ { 2 } = 8 ( y - 1 )$
D) $( x - 6 ) ^ { 2 } = - 8 ( y - 1 )$

Question 31

Find an equation for the parabola described.

-Vertex at (3, -4); focus at (3, -6)

A) $( x - 3 ) ^ { 2 } = 8 ( y + 4 )$
B) $( x - 3 ) ^ { 2 } = - 8 ( y + 4 )$
C) $( y - 4 ) ^ { 2 } = - 12 ( x + 3 )$
D) $( y - 4 ) ^ { 2 } = 12 ( x + 3 )$

Question 32

Find the vertex, focus, and directrix of the parabola. Graph the equation.

- $(y+2)^{2}=8(x+3)$

A)
vertex: $(2,3)$
focus: $(4,3)$
directrix: $x=0$



B)
$\begin{array}{l}\text { vertex: }(-3,-2) \\\text { focus: }(-1,-2) \\\text { directrix: } x=-5\end{array}$


C)
vertex: $(3,2)$
focus: $(3,4)$
directrix: $y=0$


D)
$\begin{array}{l}\text { vertex: }(-3,-2) \\\text { focus: }(-3,0) \\\text { directrix: } y=-4\end{array}$

Question 33

Find the vertex, focus, and directrix of the parabola with the given equation.

- $$( y + 1 ) ^ { 2 } = 16 ( x + 3 )$$

A) vertex: $( - 3 , - 1 )$
focus: $( - 7 , - 1 )$
$\text { directrix: } x=1$

B) vertex: $( - 1 , - 3 )$
focus: $( 3 , - 3 )$
$\text { directrix: } x=-5$

C) vertex: $( - 3 , - 1 )$
focus: $( 1 , - 1 )$
$\text { directrix: } x=-7$

D) vertex: $( 3,1 )$
focus: $( 7,1 )$
$\text { directrix: } x=-1$

Question 34

Find an equation for the parabola described.

-Vertex at (7, 8); focus at (3, 8)

A) $( y - 8 ) ^ { 2 } = - 16 ( x - 7 )$
B) $( y - 8 ) ^ { 2 } = 16 ( x - 7 )$
C) $( x - 8 ) ^ { 2 } = 20 ( y - 8 )$
D) $( x - 8 ) ^ { 2 } = - 20 ( y - 8 )$

Question 35

Find an equation for the parabola described.

-Vertex at (7, -9); focus at (3, -9)

A) $( x + 8 ) ^ { 2 } = - 4 ( y - 4 )$
B) $( x + 8 ) ^ { 2 } = 4 ( y - 4 )$
C) $( y + 4 ) ^ { 2 } = - 12 ( x - 8 )$
D) $( y + 9 ) ^ { 2 } = 16 ( x - 7 )$

Question 36

Graph the equation.

- $x^{2}=-18 y$

A)


B)


C)


D)

Question 37

Find the vertex, focus, and directrix of the parabola with the given equation.

- $(y-4)^{2}=-8(x+2)$

A)
vertex: $(-2,4)$
focus: $(0,4)$
directrix: $x=-4$

B)
$\begin{array}{l}\text { vertex: }(4,-2) \\\text { focus: }(2,-2) \\\text { directrix: } x=6\end{array}$

C)
vertex: $(2,-4)$
focus: $(0,-4)$
directrix: $x=4$

D)
vertex: $(-2,4)$
focus: $(-4,4)$
directrix: $x=0$

Question 38

Match the equation to the graph.

- $$( y - 2 ) ^ { 2 } = 6 ( x - 2 )$$

A)


B)

C)


D)

Question 39

Match the equation to the graph.

- $$( x + 2 ) ^ { 2 } = - 6 ( y + 2 )$$

A)


B)


C)


D)

Question 40

Find the vertex, focus, and directrix of the parabola with the given equation.

- $$( x - 2 ) ^ { 2 } = - 20 ( y - 3 )$$

A) vertex: $( 2,3 )$
focus: $( 2 , - 2 )$
$\text { directrix: } y=8$

B) vertex: $( - 2 , - 3 )$
focus: $( - 2 , - 8 )$
$\text { directrix: } y=2$

C) vertex: $( 2,3 )$
focus: $( 2,8 )$
$\text { directrix: } x=-2$

D) vertex: $( 3,2 )$
focus: $( 3 , - 3 )$
$\text { directrix: } y=7$




directrix: $y = 8 \quad$ directrix: $y = 2 \quad$ directrix: $x = - 2 \quad$ directrix: $y = 7$

Question 41

Solve the problem.
A satellite dish is shaped like a paraboloid of revolution. The signals that emanate from a satellite strike the
surface of the dish and are reflected to a single point, where the receiver is located. If the dish is 8 feet across at
its opening and is 2 feet deep at its center, at what position should the receiver be placed?

Question 42

Solve the problem.
A spotlight has a parabolic cross section that is 6 ft wide at the opening and 2.5 ft deep at the vertex. How far from the vertex is the focus? Round answer to two decimal places.

A) 0.21 ft
B) 0.52 ft
C) 0.26 ft
D) 0.90 ft

Question 43

Graph the equation.

- $(x+2)^{2}=8(y-1)$

A)

B)

C)

D)

Question 44

Find the center, foci, and vertices of the ellipse.

- $$\frac { x ^ { 2 } } { 81 } + \frac { y ^ { 2 } } { 9 } = 1$$

A) center at $( 0,0 )$
foci at $( - 6 \sqrt { 2 } , 0 )$ and $( 6 \sqrt { 2 } , 0 )$
vertices at $( - 9,0 ) , ( 9,0 )$

B) center at $( 0,0 )$
foci at $( 0 , - 3 )$ and $( 0,3 )$
vertices at $( 0 , - 9 ) , ( 0,9 )$

C) center at $( 0,0 )$
foci at $( 0 , - 6 \sqrt { 2 } )$ and $( 0,6 \sqrt { 2 } )$
vertices at $( 0 , - 9 ) , ( 0,9 )$

D) center at $( 0,0 )$
foci at $( - 9,0 )$ and $( 9,0 )$
vertice at $( - 81,0 ) , ( 81,0 )$

Question 45

Find the center, foci, and vertices of the ellipse.

- $$9 x ^ { 2 } + 4 y ^ { 2 } = 36$$

A) center at $( 0,0 )$
foci at $( 0,3 )$ and $( 2,0 )$
vertices at $( 0,9 )$ and $( 4,0 )$

B) center at $( 0,0 )$
foci at $( 0 , - \sqrt { 5 } )$ and $( 0 , \sqrt { 5 } )$
vertices at $( 0 , - 3 ) , ( 0,3 )$

C) center at $( 0,0 )$
foci at $( 0 , - 3 )$ and $( 0,3 )$
vertices at $( 0 , - 9 ) , ( 0,9 )$

D) center at $( 0,0 )$
foci at $( - \sqrt { 5 } , 0 )$ and $( \sqrt { 5 } , 0 )$
vertices at $( - 3,0 ) , ( 3,0 )$

Question 46

Match the graph to its equation.

-

A) $\frac { y ^ { 2 } } { 49 } + \frac { x ^ { 2 } } { 4 } = 1$

B) $\frac { x ^ { 2 } } { 49 } + \frac { y ^ { 2 } } { 4 } = 1$

C) $\frac { y ^ { 2 } } { 49 } - \frac { x ^ { 2 } } { 4 } = 1$

D) $- \frac { y ^ { 2 } } { 49 } + \frac { x ^ { 2 } } { 4 } = 1$

Question 47

Solve the problem.
A sealed-beam headlight is in the shape of a paraboloid of revolution. The bulb, which is placed at the focus, is
3 centimeters from the vertex. If the depth is to be 6 centimeters, what is the diameter of the headlight at its
opening?

Question 48

Find the center, foci, and vertices of the ellipse.

- $$\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 64 } = 1$$

A) center at $( 0,0 )$
foci at $( 0,8 )$ and $( 4,0 )$
vertices at $( 0,64 ) , ( 16,0 )$

B) center at $( 0,0 )$
foci at $( 0 , - 8 )$ and $( 0,8 )$
vertices at $( 0 , - 64 ) , ( 0,64 )$

C) center at $( 0,0 )$
foci at $( - 4 \sqrt { 3 } , 0 )$ and $( 4 \sqrt { 3 } , 0 )$
vertices at $( - 8,0 ) , ( 8,0 )$

D) center at $( 0,0 )$
foci at $( 0 , - 4 \sqrt { 3 } )$ and $( 0,4 \sqrt { 3 } )$
vertices at $( 0 , - 8 ) , ( 0,8 )$

Question 49

Find an equation for the ellipse described.

-Center at $( 0,0 )$ ; focus at $( 5,0 )$ ; vertex at $( 7,0 )$

A) $\frac { x ^ { 2 } } { 49 } + \frac { y ^ { 2 } } { 24 } = 1$

B) $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 24 } = 1$

C) $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 49 } = 1$

D) $\frac { x ^ { 2 } } { 24 } + \frac { y ^ { 2 } } { 49 } = 1$

Question 50

Solve the problem.
A reflecting telescope contains a mirror shaped like a paraboloid of revolution. If the mirror is 24 inches across at its opening and is 4 feet deep, where will the light be concentrated?

A) 0.1 in. from the vertex
B) 10.1 in. from the vertex
C) 0.2 in. from the vertex
D) 0.8 in. from the vertex

Question 51

Match the graph to its equation.

-

A) $\frac { y ^ { 2 } } { 16 } + \frac { x ^ { 2 } } { 9 } = 1$

B) $\frac { x ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 16 } = 1$

C) $\frac { y ^ { 2 } } { 16 } - \frac { x ^ { 2 } } { 9 } = 1$

D) $\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 9 } = 1$

Question 52

Find the center, foci, and vertices of the ellipse.

- $$4 x ^ { 2 } + 64 y ^ { 2 } = 256$$

A) center at $( 0,0 )$
foci at $( 0 , - 2 )$ and $( 0,2 )$
vertices at $( 0 , - 4 ) , ( 0,4 )$

B) center at $( 0,0 )$
foci at $( 0 , - 2 \sqrt { 15 } )$ and $( 0,2 \sqrt { 15 } )$
vertices at $( 0 , - 8 ) , ( 0,8 )$

C) center at $( 0,0 )$
foci at $( - 2 \sqrt { 15 } , 0 )$ and $( 2 \sqrt { 15 } , 0 )$
vertices at $( - 8,0 ) , ( 8,0 )$

D) center at $( 0,0 )$
foci at $( - 8,0 )$ and $( 8,0 )$
vertices at $( - 64,0 ) , ( 64,0 )$

Question 53

Solve the problem.
A searchlight is shaped like a paraboloid of revolution. If the light source is located 5 feet from the base along the axis of symmetry and the opening is 8 feet across, how deep should the searchlight be?

A) 4 ft
B) 0.8 ft
C) 1.6 ft
D) 3.2 ft

Question 54

Graph the equation.

- $(y-1)^{2}=-7(x+2)$

A)


B)


C)


D)

Question 55

Solve the problem.
An experimental model for a suspension bridge is built in the shape of a parabolic arch. In one section, cable runs from the top of one tower down to the roadway, just touching it there, and up again to the top of a second
Tower. The towers stand 50 inches apart. At a point between the towers and 15 inches along the road from the
Base of one tower, the cable is 1 inches above the roadway. Find the height of the towers.

A) 6.75 in.
B) 5.75 in.
C) 6.25 in.
D) 8.25 in.

Question 56

Solve the problem.
An experimental model for a suspension bridge is built in the shape of a parabolic arch. In one section, cable runs from the top of one tower down to the roadway, just touching it there, and up again to the top of a second
Tower. The towers are both 12.25 inches tall and stand 70 inches apart. Find the vertical distance from the
Roadway to the cable at a point on the road 14 inches from the lowest point of the cable.

A) 2.16 in.
B) 1.76 in.
C) 7.84 in.
D) 1.96 in.

Question 57

Solve the problem.
A bridge is built in the shape of a parabolic arch. The bridge arch has a span of 174 feet and a maximum height of 30 feet. Find the height of the arch at 15 feet from its center.

A) 3.6 ft
B) 21.8 ft
C) 0.2 ft
D) 29.1 ft

Question 58

Solve the problem.

-A reflecting telescope has a mirror shaped like a paraboloid of revolution. If the distance of the vertex to the focus is 31 feet and the distance across the top of the mirror is 66 inches, how deep is the mirror in the center?

A) $\frac { 121 } { 1984 }$ in.

B) $\frac { 363 } { 496 }$ in.

C) $\frac { 961 } { 132 }$ in.

D) $\frac { 1089 } { 124 } \mathrm { in }$ .

Question 59

Graph the equation.

- $(x+1)^{2}=-8(y-2)$

A)

B)

C)

D)

Question 60

Solve the problem.
An experimental model for a suspension bridge is built in the shape of a parabolic arch. In one section, cable runs from the top of one tower down to the roadway, just touching it there, and up again to the top of a second
Tower. The towers are both 12.25 inches tall and stand 70 inches apart. At some point along the road from the
Lowest point of the cable, the cable is 1.96 inches above the roadway. Find the distance between that point and
The base of the nearest tower.

A) 21 in.
B) 13.8 in.
C) 14.2 in.
D) 21.2 in.

Question 61

Find the center, foci, and vertices of the ellipse.

- $$\frac { ( x - 1 ) ^ { 2 } } { 36 } + \frac { ( y + 2 ) ^ { 2 } } { 9 } = 1$$

A) center at $( 1 , - 2 )$
foci at $( 1 + 3 \sqrt { 3 } , 1 ) , ( 1 - 3 \sqrt { 3 } , 1 )$
vertices at $( 6 , - 2 ) , ( - 6 , - 2 )$

B) center at $( - 2,1 )$
foci at $( - 2 + 3 \sqrt { 3 } , 1 ) , ( - 2 - 3 \sqrt { 3 } , 1 )$
vertices at $( - 5 , - 2 ) , ( 7 , - 2 )$

C) center at $( 1 , - 2 )$
foci at $( - 3 \sqrt { 3 } , - 2 ) , ( 3 \sqrt { 3 } , - 2 )$
vertices at $( 6 , - 2 ) , ( - 6 , - 2 )$

D) center at $( 1 , - 2 )$
foci at $( 1 + 3 \sqrt { 3 } , - 2 ) , ( 1 - 3 \sqrt { 3 } , - 2 )$
vertices at $( - 5 , - 2 ) , ( 7 , - 2 )$

Question 62

Find an equation for the ellipse described.

-Center $( 0,0 )$ ; major axis horizontal with length 10 ; length of minor axis is 4

A) $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 9 } = 1$

B) $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 4 } = 1$

C) $\frac { x ^ { 2 } } { 6 } + \frac { y ^ { 2 } } { 4 } = 1$

D) $\frac { x ^ { 2 } } { 100 } + \frac { y ^ { 2 } } { 16 } = 1$

Question 63

Graph the ellipse and locate the foci.

- $4 x^{2}+16 y^{2}=64$

A) foci at $( 5,0 )$ and $( - 5,0 )$


B) foci at $( \sqrt { 7 } , 0 )$ and $( - \sqrt { 7 } , 0 )$


C) foci at $( 4,0 )$ and $( - 4,0 )$


D) foci at $( 0 , \sqrt { 7 } )$ and $( 0 , - \sqrt { 7 } )$

Question 64

Find the center, foci, and vertices of the ellipse.

- $16 x ^ { 2 } + y ^ { 2 } - 256 x + 1,008 = 0$

A) $( x - 2 ) ^ { 2 } + \frac { y ^ { 2 } } { 64 } = 1$
center: $( 2,0 )$ ; foci: $( 2,3 \sqrt { 7 } ) , ( 2 , - 3 \sqrt { 7 } )$ ; vertices:( 2, $8 ), ( 2 , - 8 )$

B) $( x - 8 ) ^ { 2 } + \frac { y ^ { 2 } } { 4 } = 1$
center: $( 8,0 )$ ; foci: $( 8 , \sqrt { 3 } ) , ( 8 , - \sqrt { 3 } )$ ; vertices: $( 8,2 ) , ( 8 , - 2 )$

C) $\frac { x ^ { 2 } } { 64 } + ( y - 2 ) ^ { 2 } = 1$
center: $( 2,0 )$ ; foci: $( 2,3 \sqrt { 7 } ) , ( 2 , - 3 \sqrt { 7 } )$ ; vertices: $( 2,8 ) , ( 2 , - 8 )$

D) $\frac { x ^ { 2 } } { 4 } + ( y - 8 ) ^ { 2 } = 1$
center: $( 8,0 )$ ; foci: $( 8 , \sqrt { 3 } ) , ( 8 , - 3 \sqrt { 7 } )$ ; vertices: $( 8,2 )$ , $( 8 , - 2 )$

Question 65

Find an equation for the ellipse described.

-Center at $( 0,0 )$ ; focus at $( 0,2 )$ ; vertex at $( 0,3 )$

A) $\frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 64 } = 1$

B) $\frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 28 } = 1$

C) $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 5 } = 1$

D) $\frac { x ^ { 2 } } { 5 } + \frac { y ^ { 2 } } { 9 } = 1$

Question 66

Find an equation for the ellipse described.

-Foci at $( 0 , \pm 5 ) ; \quad \mathrm { y }$ -intercepts are $\pm 8$

A) $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 64 } = 1$

B) $\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 39 } = 1$

C) $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 39 } = 1$

D) $\frac { x ^ { 2 } } { 39 } + \frac { y ^ { 2 } } { 64 } = 1$

Question 67

Find an equation for the ellipse described.

-Center at $( 0,0 )$ ; focus at $( - 3,0 )$ ; vertex at $( 4,0 )$

A) $\frac { x ^ { 2 } } { 7 } + \frac { y ^ { 2 } } { 16 } = 1$

B) $\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 7 } = 1$

C) $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 16 } = 1$

D) $\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 48 } = 1$

Question 68

Find an equation for the ellipse described.

-Center at $( 0,0 )$ ; focus at $( - 5,0 ) ;$ vertex at $( 8,0 )$

A) $\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 60 } = 1$

B) $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 64 } = 1$

C) $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 60 } = 1$

D) $\frac { x ^ { 2 } } { 60 } + \frac { y ^ { 2 } } { 64 } = 1$

Question 69

Find an equation for the ellipse described.

-Center at $( 0,0 ) ;$ focus at $( 0 , - 2 )$ ; vertex at $( 0,6 )$

A) $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 32 } = 1$

B) $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 36 } = 1$

C) $\frac { x ^ { 2 } } { 32 } + \frac { y ^ { 2 } } { 36 } = 1$

D) $\frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 32 } = 1$

Question 70

Find an equation for the ellipse described.

-Foci at $( \pm 2,0 ) ; \quad x$ -intercepts are $\pm 7$

A) $\frac { x ^ { 2 } } { 45 } + \frac { y ^ { 2 } } { 49 } = 1$

B) $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 49 } = 1$

C) $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 45 } = 1$

D) $\frac { x ^ { 2 } } { 49 } + \frac { y ^ { 2 } } { 45 } = 1$

Question 71

Graph the ellipse and locate the foci.

- $\frac{x^{2}}{9}+\frac{y^{2}}{16}=1$

A) foci at $( \sqrt { 13 } , 0 )$ and $( - \sqrt { 13 } , 0 )$


B) foci at $( 2 \sqrt { 3 } , 0 )$ and $( - 2 \sqrt { 3 } , 0 )$


C) foci at $( 0 , \sqrt { 5 } )$ and $( 0 , - \sqrt { 5 } )$


D) foci at $( \sqrt { 5 } , 0 )$ and $( - \sqrt { 5 } , 0 )$

Question 72

Write an equation for the graph.

-

A) $\frac { ( x - 2 ) ^ { 2 } } { 4 } + \frac { ( y - 1 ) ^ { 2 } } { 9 } = 1$

B) $\frac { ( x + 2 ) ^ { 2 } } { 9 } + \frac { ( y + 1 ) ^ { 2 } } { 4 } = 1$

C) $\frac { ( x - 1 ) ^ { 2 } } { 9 } + \frac { ( y - 2 ) ^ { 2 } } { 4 } = 1$

D) $\frac { ( x - 2 ) ^ { 2 } } { 9 } + \frac { ( y - 1 ) ^ { 2 } } { 4 } = 1$

Question 73

Graph the ellipse and locate the foci.

- $$\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 9 } = 1$$

A) foci at $( \sqrt { 21 } , 0 )$ and $( - \sqrt { 21 } , 0 )$


B) foci at $( 2 \sqrt { 5 } , 0 )$ and $( - 2 \sqrt { 5 } , 0 )$


C) $\text { foci at }(2 \sqrt{3}, 0) \text { and }(-2 \sqrt{3}, 0)$


D) $\text { foci at }(0,2 \sqrt{3}) \text { and }(0,-2 \sqrt{3})$

Question 74

Find an equation for the ellipse described.

-Focus at $( - 3,0 )$ ; vertices at $( \pm 5,0 )$

A) $\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 25 } = 1$

B) $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 16 } = 1$

C) $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 25 } = 1$

D) $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 16 } = 1$

Question 75

Find an equation for the ellipse described.

-Focus at $( 0 , - 4 )$ ; vertices at $( 0 , \pm 8 )$

A) $\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 48 } = 1$

B) $\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 48 } = 1$

C) $\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 64 } = 1$

D) $\frac { x ^ { 2 } } { 48 } + \frac { y ^ { 2 } } { 64 } = 1$

Question 76

Graph the ellipse and locate the foci.

- $16 x^{2}+9 y^{2}=144$

A) foci at $( 5,0 )$ and $( - 5,0 )$


B) $\text { foci at }(4,0) \text { and }(-4,0)$


C) foci at $( \sqrt { 7 } , 0 )$ and $( - \sqrt { 7 } , 0 )$


D) foci at $( 0 , \sqrt { 7 } )$ and $( 0 , - \sqrt { 7 } )$

Question 77

Graph the equation.

- $$\frac { ( x - 1 ) ^ { 2 } } { 9 } + \frac { ( y + 1 ) ^ { 2 } } { 4 } = 1$$

A)


B)


C)


D)

Question 78

Find the center, foci, and vertices of the ellipse.

- $$2 x ^ { 2 } + 5 y ^ { 2 } - 12 x + 60 y + 188 = 0$$

A) $\frac { ( x - 3 ) ^ { 2 } } { 2 } + \frac { ( y + 6 ) ^ { 2 } } { 5 } = 1$
center: $( - 3,6 )$ ; foci: $( - 1.3,6 ) , ( - 4.7,6 )$ ; vertices: $( - 5.2,6 ) , ( - 0.8,6 )$

B) $\frac { ( x - 3 ) ^ { 2 } } { 5 } + \frac { ( y + 6 ) ^ { 2 } } { 2 } = 1$
center: $( 3 , - 6 )$ ; foci: $( 4.7 , - 6 ) , ( 1.3 , - 6 )$ ; vertices: $( 5.2 , - 6 ) , ( 0.8 , - 6 )$

C) $\frac { ( x - 3 ) ^ { 2 } } { 5 } + \frac { ( y + 6 ) ^ { 2 } } { 2 } = 1$
center: $( - 3,6 )$ ; foci: $( - 1.3,6 ) , ( - 4.7,6 )$ ; vertices: $( - 5.2,6 ) , ( - 0.8,6 )$

D) $\frac { ( x - 3 ) ^ { 2 } } { 2 } + \frac { ( y + 6 ) ^ { 2 } } { 5 } = 1$
center: $( 3 , - 6 )$ ; foci: $( 4.7 , - 6 ) , ( 1.3 , - 6 )$ ; vertices: $( 5.2 , - 6 ) , ( 0.8 , - 6 )$

Question 79

Find an equation for the ellipse described.

-Center at $( 0,0 ) ;$ focus at $( 0,5 )$ ; vertex at $( 0 , - 7 )$

A) $\frac { x ^ { 2 } } { 24 } + \frac { y ^ { 2 } } { 49 } = 1$

B) $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 24 } = 1$

C) $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 49 } = 1$

D) $\frac { x ^ { 2 } } { 49 } + \frac { y ^ { 2 } } { 24 } = 1$

Question 80

Find the center, foci, and vertices of the ellipse.

- $$16 ( \mathrm { x } + 2 ) ^ { 2 } + 9 ( \mathrm { y } - 1 ) ^ { 2 } = 144$$

A) center at $( - 1,1 )$
foci at $( - 1,1 - \sqrt { 7 } ) , ( - 1,1 + \sqrt { 7 } )$
vertices at $( - 1,5 ) , ( - 1 , - 3 )$

B) center at $( 1 , - 2 )$
foci at $( 1 , - 2 - \sqrt { 7 } ) , ( 1 , - 2 + \sqrt { 7 } )$
vertices at $( 1,5 ) , ( 1 , - 3 )$

C) center at $( 2,1 )$
foci at $( 2,1 - \sqrt { 7 } ) , ( 2,1 + \sqrt { 7 } )$
vertices at $( 2,5 ) , ( 2 , - 3 )$

D) center at $( - 2,1 )$
foci at $( - 2,1 - \sqrt { 7 } ) , ( - 2,1 + \sqrt { 7 } )$
vertices at $( - 2,5 ) , ( - 2 , - 3 )$