ANSWER
[tex]( {y - 8)}^{2} = - 28(x + 5)[/tex]
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:
[tex]( {y - k)}^{2} = 4p(x - h)[/tex]
where (h,k)=(-5,8) is the vertex.
[tex] |p| = | - 2 - 5| = 7[/tex]
[tex]p = \pm7[/tex]
But the parabola opens to the left.
p=-7
The equation now becomes
[tex]( {y - 8)}^{2} = 4( - 7)(x - - 5)[/tex]
[tex]( {y - 8)}^{2} = - 28(x + 5)[/tex]
