Parabolas (Sec 9-4)

Question 1

When the focus and directrix are used to derive the equation of a parabola, two distances were set equal to each other. = The distance between the directrix and is set equal to the distance between the and the same point on the parabola.

Revolt · Accepted Answer

a point on the parabola; Selection 1: a point on the parabola; Selection 2: focus

Question 2

Question 2

Revolt · Accepted Answer

focus

Question 3

If the equation is further simplified, which equation for a parabola does it become?

Revolt · Accepted Answer

x2 = 4py

Question 4

Lauren describes a parabola where the focus has a positive, nonzero x coordinate. Which parabola(s) could Lauren be describing? Check all that apply.x2 = 4yx2 = –6yy2 = x y2 = 10xy2 = –3xy2 = 5x

Revolt · Accepted Answer

y2 = x; y2 = 10x; y2 = 5x

Question 5

The shape of a satellite dish can be described as parabolic. Satellite dishes are this shape because radio waves are reflected from the surface of the dish and received into the focus. If the graph of the satellite dish is given by the equation x2 = 8y, what are the coordinates of the focus? (, )

Revolt · Accepted Answer

Part 1: 0; Part 2: 2

Question 6

Which graph represents the function y2 = −16x?

Revolt · Accepted Answer

[Image: On a coordinate plane, a parabola opens to the lef...]

Question 7

The parabola has a focus at (−3, 0) and directrix x = 3. What is the correct equation for the parabola?

Revolt · Accepted Answer

y2 = −12x

Question 8

Which statements are true for the equation x2 = −4y? Check all that apply.The axis of symmetry is x = 0.The focus is at (0, –1).The parabola opens up.The parabola opens right.The value of p = −1.The equation for the directrix is y = 0.

Revolt · Accepted Answer

The axis of symmetry is x = 0.; The focus is at (0, –1).; The value of p = −1.

Question 9

If the directrix of a parabola is the horizontal line y = 3, what is true of the parabola?

Revolt · Accepted Answer

The focus is at (0, –3), and the equation for the parabola is x2 = –12y.

Question 10

Describe the key features of the parabola y2 = 8x.

Revolt · Accepted Answer

The parabola y^2 = 8x is in the form y^2 = 4px, where 4p = 8, so p = 2. Since p > 0 and the equation is in terms of y^2, the parabola opens to the right. The vertex is at the origin (0, 0). The focus is at (p, 0), which is (2, 0). The directrix is the vertical line x = -p, which is x = -2. The axis of symmetry is the x-axis, or y = 0.

Parabolas (Sec 9-4) Answers

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