Conic Sections: Parabolas — Test

Question 1

A parabola can be represented by the equation x2 = 2y.

Revolt · Accepted Answer

focus: ; directrix: y =

Question 2

Which is the standard form of the equation of the parabola that has a vertex of (3, 1) and a directrix of x = –2?

Revolt · Accepted Answer

✓ Correct

Question 3

Fabio is designing a flashlight that uses a parabolic reflecting mirror and a light source. The shape of the mirror can be modeled by , where x and y are measured in inches. Where is the focus of the flashlight?

Revolt · Accepted Answer

(–2, –0.5)

Question 4

What is the radius of a circle whose equation is (x + 5)2 + (y – 3)2 = 42?

Revolt · Accepted Answer

4 units

Question 5

A parabola with a vertex at (0,0) has a directrix that crosses the negative part of the y-axis.

Revolt · Accepted Answer

x2 = 4y

Question 6

A general formula for a parabola is x2=4py.What is the value of p in the equation x2=12y?

Revolt · Accepted Answer

p=3

Question 7

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

Revolt · Accepted Answer

radius.

Question 8

A parabola and its focus are shown on the graph. The vertex of the parabola is at (0,0).

Revolt · Accepted Answer

x = –3

Question 9

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 x2 + y2 – 8x – 6y + 24 = 0.

Revolt · Accepted Answer

(x – 4)2 + (y – 3)2 = 2²

Question 10

Aramis is adjusting a satellite because he finds it is not focusing the incoming radio waves perfectly. The shape of his satellite can be modeled by , where x and y are modeled in inches. He realizes that the static is a result of the feed antenna shifting slightly off the focus point. Where should the feed antenna be placed?

Revolt · Accepted Answer

0.75 in. above the vertex ✓ Correct

Conic Sections: Parabolas — Test Answers

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