Question

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Answer 1

ANSWER

$( {y - 8)}^{2} = - 28(x + 5)$

EXPLANATION

The given parabola has directrix x=2.

This implies that, the parabola is opens in the direction of the negative x-axis because it must open in a negative direction to the directrix.

The equation of such parabola is of the form:

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

where (h,k)=(-5,8) is the vertex.

$|p| = | - 2 - 5| = 7$

$p = \pm7$

But the parabola opens to the left.

p=-7

The equation now becomes

$( {y - 8)}^{2} = 4( - 7)(x - - 5)$

$( {y - 8)}^{2} = - 28(x + 5)$