Conic Sections — Test Answers

25 verified answers

Which equation represents this ellipse?

the fraction with numerator open paren x plus 6 close paren squared and denominator 49 plus the fraction with numerator open paren y plus 2 close paren squared and denominator 9 is equal to 1

the fraction with numerator open paren y minus 6 close paren squared and denominator 49 plus the fraction with numerator open paren x minus 2 close paren squared and denominator 9 is equal to 1

the fraction with numerator open paren y plus 6 close paren squared and denominator 49 plus the fraction with numerator open paren x plus 2 close paren squared and denominator 9 is equal to 1

the fraction with numerator open paren x minus 6 close paren squared and denominator 49 plus the fraction with numerator open paren y minus 2 close paren squared and denominator 9 is equal to 1

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Which points are the vertices of the ellipse?

points cap q and cap r

points cap n and cap p

points cap s and cap t

points cap o and cap p

What are the coordinates of a vertex of the hyperbola?

open paren negative 3 comma 0 close paren

open paren 0 comma 5 close paren

open paren 0 comma 0 close paren

open paren 0 comma negative 4 close paren

Which completes the work correctly?

open paren x plus 3 close paren squared plus open paren y plus 2 close paren squared is equal to 4 squared , so the center is negative 3 comma negative 2 .

open paren x plus 3 close paren squared plus open paren y plus 2 close paren squared is equal to 4 squared , so the center is 3 comma 2 .

open paren x minus 3 close paren squared plus open paren y minus 2 close paren squared is equal to 4 squared , so the center is negative 3 comma negative 2 .

open paren x minus 3 close paren squared plus open paren y minus 2 close paren squared is equal to 4 squared , so the center is 3 comma 2 .

Which equation represents the parabola shown on the graph?

x squared is equal to 6 y

y squared is equal to 1 point 5 x

y squared is equal to 6 x

x squared is equal to 1 point 5 y

What is the equation of the directrix of the parabola?

y is equal to 3

x is equal to 3

y is equal to negative 3

x is equal to negative 3

Which equation represents a hyperbola with a center at open paren 0 comma 0 close paren , a vertex at open paren negative 48 comma 0 close paren , and a focus at open paren 50 comma 0 close paren ?

the fraction with numerator y squared and denominator 50 squared minus the fraction with numerator x squared and denominator 14 squared is equal to 1

the fraction with numerator y squared and denominator 48 squared minus the fraction with numerator x squared and denominator 14 squared is equal to 1

the fraction with numerator x squared and denominator 50 squared minus the fraction with numerator y squared and denominator 14 squared is equal to 1

the fraction with numerator x squared and denominator 48 squared minus the fraction with numerator y squared and denominator 14 squared is equal to 1

What are the vertices of the hyperbola whose equation is the fraction with numerator open paren x plus 7 close paren squared and denominator 25 minus the fraction with numerator open paren y minus 8 close paren squared and denominator 36 is equal to 1 ?

open paren negative 12 comma 8 close paren and open paren negative 2 comma 8 close paren

open paren negative 13 comma 8 close paren and open paren negative 1 comma 8 close paren

open paren negative 7 comma 2 close paren and open paren negative 7 comma 14 close paren

open paren negative 7 comma 3 close paren and open paren negative 7 comma 13 close paren

What is the equation of the directrix to the right of the center of the fraction with numerator open paren x minus 1 close paren squared and denominator 9 minus the fraction with numerator open paren y minus 2 close paren squared and denominator 16 is equal to 1 ? Express the answer in decimal format.

Answer:

2.8

An ellipse has vertices along the major axis at open paren 0 comma 1 close paren and open paren 0 comma negative 9 close paren The foci of the ellipse are located at open paren 0 comma negative 1 close paren and open paren 0 comma negative 7 close paren The equation of the ellipse is in the form. the fraction with numerator open paren y minus k close paren squared and denominator A squared plus the fraction with numerator open paren x minus h close paren squared and denominator b squared is equal to 1 Which is a correct value for one of the variables shown in the equation?

A is equal to 10

k is equal to 0

b is equal to 4

h is equal to 3

What are the foci of the hyperbola whose equation is the fraction with numerator open paren y minus 2 close paren squared and denominator 64 minus the fraction with numerator open paren x minus 4 close paren squared and denominator 36 is equal to 1 ?

open paren negative 6 comma 2 close paren and open paren 14 comma 2 close paren

open paren 4 comma negative 8 close paren and open paren 4 comma 12 close paren

open paren negative 4 comma 2 close paren and open paren 12 comma 2 close paren

open paren 4 comma negative 6 close paren and open paren 4 comma 10 close paren

A parabola can be represented by the equation x squared is equal to 2 y What are the coordinates of the focus and the equation of the directrix?

focus: open paren 1 half comma 0 close paren ; directrix: x is equal to negative 1 half

focus: open paren 0 comma 1 half close paren ; directrix: y is equal to negative 1 half

focus: open paren 8 comma 0 close paren ; directrix: x is equal to negative 8

focus: open paren 0 comma 8 close paren ; directrix: y is equal to negative 8

A point is on a circle if the distance from the center of the circle to the point is equal to the

radius.

circumference.

area.

diameter.

A general formula for a parabola is x squared is equal to 4 p y What is the value of p in the equation x squared is equal to 12 y ?

p is equal to 6

p is equal to 3

p is equal to 12

p is equal to 4

What is the radius of a circle whose equation is open paren x plus 5 close paren squared plus open paren y minus 3 close paren squared is equal to 4 squared ?

16 units

4 units

8 units

2 units

Consider a circle whose equation is x squared plus y squared minus 2 x minus 8 is equal to 0 Which statements are true? Choose three correct answers.

The center of the circle lies on the y -axis.

The radius of this circle is the same as the radius of the circle whose equation is x squared plus y squared is equal to 9 .

The center of the circle lies on the x -axis.

The standard form of the equation is open paren x minus 1 close paren squared plus y squared is equal to 3 .

The radius of the circle is 3 units.

Which graph represents the hyperbola the fraction with numerator x squared and denominator 3 squared minus the fraction with numerator y squared and denominator 8 squared is equal to 1 ?

Image with description A four-quadrant coordinate plane. A hyperbola is shown centered at the origin. The transverse axis has endpoints at (negative 8 comma 0) and (8 comma 0). The branches of the hyperbola open left and right. A dashed box is shown around the points (negative 8 comma 0), (0 comma 3), (8 comma 0), and (0 comma negative 3).

Image with description A four-quadrant coordinate plane. A hyperbola is shown centered at the origin. The transverse axis has endpoints at (negative 3 comma 0) and (3 comma 0). The branches of the hyperbola open left and right. A dashed box is shown around the points (negative 3 comma 0), (0 comma 8), (3 comma 0), and (0 comma negative 8).

Image with description A four-quadrant coordinate plane. A hyperbola is shown centered at the origin. The transverse axis has endpoints at (0 comma negative 8) and (0 comma 8). The branches of the hyperbola open up and down. A dashed box is shown around the points (negative 3 comma 0), (0 comma 8), (3 comma 0), and (0 comma negative 8).

Image with description A four-quadrant coordinate plane. A hyperbola is shown centered at the origin. The transverse axis has endpoints at (0 comma negative 3) and (0 comma 3). The branches of the hyperbola open up and down. A dashed box is shown around the points (negative 8 comma 0), (0 comma 3), (8 comma 0), and (0 comma negative 3).

Which equation represents the circle described? The radius is 2 units. The center is the same as the center of a circle whose equation is x squared plus y squared minus 8 x minus 6 y plus 24 is equal to 0

open paren x minus 4 close paren squared plus open paren y minus 3 close paren squared is equal to 2 squared

open paren x plus 4 close paren squared plus open paren y plus 3 close paren squared is equal to 2 squared

open paren x plus 4 close paren squared plus open paren y plus 3 close paren squared is equal to 2

open paren x minus 4 close paren squared plus open paren y minus 3 close paren squared is equal to 2

A parabola with a vertex at open paren 0 comma 0 close paren has a directrix that crosses the negative part of the y -axis. Which could be the equation of the parabola?

x squared is equal to 4 y

y squared is equal to 4 x

x squared is equal to negative 4 y

y squared is equal to negative 4 x

Which lines are the directrices of the ellipse?

y is equal to negative 3 point 2 5 and y is equal to 9 point 2 5

y is equal to negative 4 point 2 5 and y is equal to 8 point 2 5

x is equal to negative 4 point 2 5 and x is equal to 8 point 2 5

x is equal to negative 3 point 2 5 and x is equal to 9 point 2 5

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Conic Sections — Test Answers

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