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

ANSWER

C.

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;

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

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

Hence, we the equation of the parabola becomes,

D.  (y − 5)2 = -8x

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