Deck 10: Conic Sections; More Graphing

Question 1

The standard form for the equation of a(n) ___________ is $y = a ( x - h ) ^ { 2 } + k$ .

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

Answer 1

parabola

Question 2

Give the vertices of the ellipse with equation $\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 1 } = 1$ .

A) $( 4,0 )$ and $( - 4,0 )$
B) $( 0,4 )$ and $( 0 , - 4 )$
C) $( 1,0 )$ and $( - 1,0 )$
D) $( 0,1 )$ and $( 0 , - 1 )$

Answer 2

$( 4,0 )$ and $( - 4,0 )$

Question 3

Describe the ellipse which is the graph of the equation $\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 9 } = 1$ .

A) vertical; vertices: $( 0,3 ) , ( 0 , - 3 )$
B) horizontal; vertices: $( 16,0 ) , ( - 16,0 )$
C) vertical; vertices: $( 0,9 ) , ( 0,9 )$
D) horizontal; vertices: $( 4,0 ) , ( - 4,0 )$

Answer 3

horizontal; vertices: $( 4,0 ) , ( - 4,0 )$

Question 4

Match the equation with the type of conic section .

- $x = y ^ { 2 } - 3 y + 7$

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

Question 5

A(n) __________ is the set of all points in a plane for which the sum of the distances from two fixed points is a constant.

Question 6

The graph of the equation is a(n) _________.

Question 7

Graph: $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 25 } = 1$

A)
B)
C)
D)

Question 8

The line segment joining the vertices of an ellipse is called the __________ of the ellipse.

Question 9

An ellipse is the set of all points in a plane for which the _________ of the distances from two fixed points is a constant.

A) product
B) quotient
C) sum
D) difference

Question 10

The midpoint of the major axis of an ellipse is the __________ of the ellipse.

Question 11

Match the graph with the correct equation:

A) $\frac { x ^ { 2 } } { 16 } + \frac { ( y + 2 ) ^ { 2 } } { 9 } = 1$
B) $\frac { x ^ { 2 } } { 4 } + \frac { ( y - 2 ) ^ { 2 } } { 3 } = 1$
C) $\frac { x ^ { 2 } } { 4 } + \frac { ( y + 2 ) ^ { 2 } } { 3 } = 1$
D) $\frac { x ^ { 2 } } { 16 } + \frac { ( y - 2 ) ^ { 2 } } { 9 } = 1$

Question 12

The arch of an underpass is a part of an ellipse. Find the equation of the ellipse.

Question 13

Match the equation with the type of conic section .

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

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

Question 14

Determine the type of graph defined by $x ^ { 2 } + y ^ { 2 } = 92$ .

A) parabola
B) ellipse
C) circle

Question 15

Find two points on the graph of by letting and finding the corresponding values of y .

Question 16

Describe the ellipse which is the graph of the equation $\frac { ( x - 1 ) ^ { 2 } } { 9 } + \frac { ( y + 6 ) ^ { 2 } } { 4 } =1$ .

A) center: $( 1 , - 6 )$ ; vertices: $( - 2 , - 6 )$ , $( 4 , - 6 )$
B) center: $( - 1,6 )$ ; vertices: $( - 3,6 )$ , $( 2,6 )$
C) center: $( 1 , - 6 )$ ; vertices: $( 3,0 )$ , $( - 3,0 )$
D) center: $( 1 , - 6 )$ ; vertices: $( 0,2 )$ , $( 0 , - 2 )$

Question 17

Match the equation with the type of conic section .

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

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

Question 18

What is the equation of the ellipse?

Question 19

Match the equation with the type of conic section .

- $2 ( x - 1 ) ^ { 2 } + 8 ( y + 5 ) ^ { 2 } = 32$

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

Question 20

In the graph, and are the __________ of the ellipse. Each one is called a(n) __________ of the ellipse.

Question 21

The midpoint of the major axis of an ellipse is the __________ of the ellipse.

Question 22

The line segment joining the vertices of an ellipse is called the __________ of the ellipse.

Question 23

What is the equation of the ellipse?

Question 24

Graph the equation.

Question 25

Graph the equation.

Question 26

A(n) __________ is the set of all points in a plane for which the sum of the distances from two fixed points is a constant.

Question 27

In the graph, and are the __________ of the ellipse. Each one is called a(n) __________ of the ellipse.

Question 28

Graph the equation.

Question 29

Graph the equation.

Question 30

What is the equation of the ellipse?

Question 31

Graph the equation.

Question 32

What is the equation of the ellipse?

Question 33

Graph the equation.

Question 34

Graph the equation.

Question 35

Graph the equation.

Question 36

In the graph, and are the __________ of the ellipse. Each one is called a(n) __________ of the ellipse.

Question 37

Graph the equation.

Question 38

The arch of an underpass is a part of an ellipse. Find the equation of the ellipse.

Question 39

Graph the equation.

Question 40

Determine whether the equation, when graphed, will be a circle, a parabola, or an ellipse.

Question 41

Determine the type of graph defined by $x ^ { 2 } = 144 + 16 y ^ { 2 }$ .

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

Question 42

Determine the type of graph defined by $x ^ { 2 } = 100 - 25 y$ .

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

Question 43

The extended diagonals of the central rectangle are _________ of the hyperbola.

Question 44

Describe the hyperbola which is the graph of the equation $\frac { y ^ { 2 } } { 9 } - \frac { ( x + 4 ) ^ { 2 } } { 49 } = 1$ .

A) center: $( 0 , - 4 )$ ; vertices: $( 0,3 )$ , $( 0 , - 3 )$
B) center: $( - 4,0 )$ ; vertices: $( - 4,3 )$ , $( - 4 , - 3 )$
C) center: $( 4,0 )$ ; vertices: $( 4,3 )$ , $( 4 , - 3 )$
D) center: $( - 4,0 )$ ; vertices: $( 0,7 )$ , $( 0,4 )$

Question 45

Find the vertices for $\frac { y ^ { 2 } } { 4 } - \frac { x ^ { 2 } } { 16 } = 1$ .

A) $( 2,0 )$ ; $( - 2,0 )$
B) $( 0,2 )$ ; $( 0 , - 2 )$
C) $( 0,4 )$ ; $( 0 , - 4 )$
D) $( 4,0 )$ ; $( - 4,0 )$

Question 46

Write the equation of the ellipse in standard form. Then graph it. Standard form:__________________

Question 47

Write in standard form of the equation of an ellipse. Give the values for a and b.

Question 48

Write the equation in the standard form of the equation of an ellipse.

Question 49

Write $x ^ { 2 } - 2 x - y ^ { 2 } + 6 y = 24$ in standard form.

A) $\frac { ( x - 1 ) ^ { 2 } } { 16 } - \frac { ( y + 3 ) ^ { 2 } } { 16 } = 1$
B) $\frac { ( x - 1 ) ^ { 2 } } { 16 } - \frac { ( y - 3 ) ^ { 2 } } { 16 } = 1$
C) $\frac { ( x - 1 ) ^ { 2 } } { 24 } - \frac { ( y + 3 ) ^ { 2 } } { 24 } = 1$
D) $\frac { ( x - 1 ) ^ { 2 } } { 24 } - \frac { ( y - 3 ) ^ { 2 } } { 24 } = 1$

Question 50

What happens to the graph of the equation when ?

Question 51

The standard form for the equation of a(n) ___________ is .

Question 52

Find the center of the ellipse graphed below. What are a and b ?
Center:_________ a = ______ b =______

Question 53

Match the graph with the correct equation:

A) $\frac { y ^ { 2 } } { 9 } - \frac { x ^ { 2 } } { 4 } = 1$
B) $\frac { y ^ { 2 } } { 3 } - \frac { x ^ { 2 } } { 2 } = 1$
C) $\frac { x ^ { 2 } } { 2 } - \frac { y ^ { 2 } } { 3 } = 1$
D) $\frac { x ^ { 2 } } { 4 } - \frac { y ^ { 2 } } { 9 } = 1$

Question 54

A __________ is the set of all points in a plane for which the difference of the distances from two fixed points is a constant.

Question 55

Determine the type of graph defined by $25 x ^ { 2 } = 125 - 25 y ^ { 2 }$ .

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

Question 56

Determine the type of graph defined by $x ^ { 2 } = 100 - 25 y ^ { 2 }$ .

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

Question 57

The two-branch curve graphed below is a __________.

Question 58

Find two points on the graph of by letting and finding the corresponding values of y .

Question 59

In the graph below, and are the __________ of the hyperbola.

Question 60

Find the x -intercept(s) for $\frac { x ^ { 2 } } { 36 } - \frac { y ^ { 2 } } { 81 } = 1$

A) $( 0,6 )$ , $( 0 , - 6 )$
B) $( 9,0 )$ , $( - 9,0 )$
C) $( 6,0 )$ , $( - 6,0 )$
D) $( 0,9 )$ , $( 0 , - 9 )$

Question 61

What is the equation of the hyperbola graphed below?

Question 62

Graph the hyperbola.

Question 63

Graph the hyperbola.

Question 64

Graph the hyperbola.

Question 65

Graph the hyperbola.

Question 66

Determine whether the equation, when graphed, will be a circle , a parabola , an ellipse , or a hyperbola .

Question 67

In the graph below, and are the __________ of the hyperbola.

Question 68

Graph the equation.

Question 69

Graph the hyperbola.

Question 70

A(n) __________ is the set of all points in a plane for which the difference of the distances from two fixed points is a constant.

Question 71

Graph the hyperbola.

Question 72

Determine whether the equation, when graphed, will be a circle , a parabola , an ellipse , or a hyperbola .

Question 73

The position of a sonic boom caused by the faster-than-sound aircraft is the hyperbola in the coordinate system shown. How wide is the hyperbola 2 units from its vertex?

Question 74

Graph the hyperbola.

Question 75

What is the equation of the hyperbola?

Question 76

Graph the hyperbola.

Question 77

Determine whether the equation, when graphed, will be a circle , a parabola , an ellipse , or a hyperbola .

Question 78

Graph the hyperbola.

Question 79

Graph the equation.

Question 80

The two-branch curve graphed below is __________.