What is the equation of a parabola whose vertex is (0, 5) and whose directrix is x = 2? A. y2 = 8(x − 5) B. 8(y − 5) = x2 C. (y − 5)2 = 8x D. (y − 5)2 = -8x

Question

asked Dec 5, 2020 121k views

2 Answers

Jasongonzales · Answer 1 · 2020-12-09T09:48:19+0000

ANSWER

C.

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

Step-by-step explanation

It was given that, the vertex of the parabola is (0,5).

The directrix of this parabola is x=2.

The directrix tells us that, the parabola will open horizontally in the positive x-axis direction.

Hence the equation of this parabola is of the form;

${(y - k)}^(2) = 4p(x - h)$

we plug in the vertex h=0, k=5 to get,

${(y - 5)}^(2) = 4p(x - 0)$

p is the distance from the vertex to the directrix, which is

p = 2 - 0 = 2

Hence, we the equation of the parabola becomes,

${(y - 5)}^(2) = 4 * 2(x - 0)$

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