Question 1

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

Accepted Answer

The standard form $y = a(x - h)^2 + k$ represents a parabola, where (h, k) is the vertex of the parabola and "a" determines the direction and width of the parabola.

Question 2

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

Accepted Answer

The vertices of an ellipse given by the equation $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ are located at $(\pm a, 0)$ along the x-axis and $(0, \pm b)$ along the y-axis. For the given equation, $a^2 = 16$ and $b^2 = 1$, so $a = 4$ and $b = 1$. Therefore, the vertices along the x-axis are $(4,0)$ and $(-4,0)$.

Question 3

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

Accepted Answer

The given equation is in the standard form of an ellipse, $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$, where $a^2 = 16$ and $b^2 = 9$. This means $a = 4$ and $b = 3$, indicating the major axis is along the x-axis (horizontal) and the vertices are at $(\pm a, 0)$ or $(\pm 4, 0)$.

Question 4

Match the equation  with the type of conic section .
-$x = y ^ { 2 } - 3 y + 7$

Accepted Answer

The given equation can be rewritten in the form $y^2 - 3y = x - 7$, which is a variation of the standard form of a parabola, indicating that the graph is a 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.

Accepted Answer

The answer of A(n) __________ is the set of all...

Question 6

The graph of the equation $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 16 } = 1$ is a(n) _________.

Accepted Answer

The answer of The graph of the equation \(\frac {...

Question 7

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

Accepted Answer

The answer of Graph: \(\frac { x ^ { 2...

Question 8

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

Accepted Answer

The answer of The line segment joining the vertices of...

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.

Accepted Answer

The definition of an ellipse is that it is the set of all points in a plane such that the sum of the distances from two fixed points (called foci) is a constant. Therefore, the correct choice is C, as it describes the sum of distances from the foci.

Question 10

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

Accepted Answer

The answer of The midpoint of the major axis of...

Question 11

Match the graph with the correct equation:

Accepted Answer

The answer of Match the graph with the correct equation:...

Question 12

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

Accepted Answer

The answer of The arch of an underpass is a...

Question 13

Match the equation  with the type of conic section .
-$\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 9 } = 1$

Accepted Answer

The answer of Match the equation  with the type...

Question 14

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

Accepted Answer

This equation represents a circle with a radius of $\sqrt{92}$, centered at the origin (0,0).

Question 15

Find two points on the graph of $\frac { x ^ { 2 } } { 400 } + \frac { y ^ { 2 } } { 16 } = 1$ by letting x=5 and finding the corresponding values of y .

Accepted Answer

The answer of Find two points on the graph of...

Question 16

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

Accepted Answer

The center of the ellipse is given by the point $(h, k)$ in the general equation $\frac{(x-h)^2}{a^2} + \frac{(y-k)^2}{b^2} = 1$, which is $(1, -6)$ for this equation. The vertices along the x-axis are found by adding and subtracting the square root of the denominator under the $x$ term ($\sqrt{9} = 3$) from the x-coordinate of the center, resulting in vertices at $(1-3, -6) = (-2, -6)$ and $(1+3, -6) = (4, -6)$.

Question 17

Match the equation  with the type of conic section .
-$( x - 3 ) ^ { 2 } + ( y + 3 ) ^ { 2 } = 16$

Accepted Answer

The equation $(x - 3)^2 + (y + 3)^2 = 16$ represents a circle because it is in the form $(x - h)^2 + (y - k)^2 = r^2$, where $(h, k)$ is the center of the circle and $r$ is the radius.

Question 18

What is the equation of the ellipse?

Accepted Answer

The answer of What is the equation of the ellipse?
...

Question 19

Match the equation  with the type of conic section .
-$2 ( x - 1 ) ^ { 2 } + 8 ( y + 5 ) ^ { 2 } = 32$

Accepted Answer

The given equation can be rewritten in the standard form of an ellipse by dividing through by 32, resulting in $\frac{(x-1)^2}{16} + \frac{(y+5)^2}{4} = 1$, which is the equation of an ellipse.

Question 20

In the graph, $\log _ { 7 } \frac { x y } { 7 }$ and $\log _ { 7 } x + \log _ { 7 } y - 1$ are the __________ of the ellipse. Each one is called a(n) __________ of the ellipse. $\log _ { 7 } x - \log _ { 7 } y + 1$

Accepted Answer

The answer of In the graph, \(\log _ { 7...

Quiz 10: Conic Sections; More Graphing

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

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

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

Match the equation with the type of conic section . - $x = y ^ { 2 } - 3 y + 7$

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.

The graph of the equation $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 16 } = 1$ is a(n) _________.

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

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

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

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

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

Match the equation with the type of conic section . - $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 9 } = 1$

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

Find two points on the graph of $\frac { x ^ { 2 } } { 400 } + \frac { y ^ { 2 } } { 16 } = 1$ by letting x=5 and finding the corresponding values of y .

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

Match the equation with the type of conic section . - $( x - 3 ) ^ { 2 } + ( y + 3 ) ^ { 2 } = 16$

What is the equation of the ellipse?

Match the equation with the type of conic section . - $2 ( x - 1 ) ^ { 2 } + 8 ( y + 5 ) ^ { 2 } = 32$

In the graph, $\log _ { 7 } \frac { x y } { 7 }$ and $\log _ { 7 } x + \log _ { 7 } y - 1$ are the of the ellipse. Each one is called a(n) of the ellipse. $\log _ { 7 } x - \log _ { 7 } y + 1$

Quiz 10: Conic Sections; More Graphing

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

Give the vertices of the ellipse with equation x216+y21=1\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 1 } = 116x2​+1y2​=1 .

Describe the ellipse which is the graph of the equation x216+y29=1\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 9 } = 116x2​+9y2​=1 .

Match the equation with the type of conic section . - x=y2−3y+7x = y ^ { 2 } - 3 y + 7x=y2−3y+7

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.

The graph of the equation x29+y216=1\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 16 } = 19x2​+16y2​=1 is a(n) _________.

Graph: x24+y225=1\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 25 } = 14x2​+25y2​=1

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

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

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

Match the graph with the correct equation:

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

Match the equation with the type of conic section . - x24+y29=1\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 9 } = 14x2​+9y2​=1

Determine the type of graph defined by x2+y2=92x ^ { 2 } + y ^ { 2 } = 92x2+y2=92 .

Find two points on the graph of x2400+y216=1\frac { x ^ { 2 } } { 400 } + \frac { y ^ { 2 } } { 16 } = 1400x2​+16y2​=1 by letting x=5 and finding the corresponding values of y .

Describe the ellipse which is the graph of the equation (x−1) 29+(y+6) 24=1\frac { ( x - 1 ) ^ { 2 } } { 9 } + \frac { ( y + 6 ) ^ { 2 } } { 4 } =19(x−1) 2​+4(y+6) 2​=1 .

Match the equation with the type of conic section . - (x−3) 2+(y+3) 2=16( x - 3 ) ^ { 2 } + ( y + 3 ) ^ { 2 } = 16(x−3) 2+(y+3) 2=16

What is the equation of the ellipse?

Match the equation with the type of conic section . - 2(x−1) 2+8(y+5) 2=322 ( x - 1 ) ^ { 2 } + 8 ( y + 5 ) ^ { 2 } = 322(x−1) 2+8(y+5) 2=32

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

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

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

Match the equation with the type of conic section . - $x = y ^ { 2 } - 3 y + 7$

The graph of the equation $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 16 } = 1$ is a(n) _________.

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

Match the equation with the type of conic section . - $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 9 } = 1$

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

Find two points on the graph of $\frac { x ^ { 2 } } { 400 } + \frac { y ^ { 2 } } { 16 } = 1$ by letting x=5 and finding the corresponding values of y .

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

Match the equation with the type of conic section . - $( x - 3 ) ^ { 2 } + ( y + 3 ) ^ { 2 } = 16$

Match the equation with the type of conic section . - $2 ( x - 1 ) ^ { 2 } + 8 ( y + 5 ) ^ { 2 } = 32$