Write the equation for a parabola with a focus at (7, 2) and a directrix at y = -2.
y =

The focus to vertex distance is (2-(-2))/2 = 2 and the parabola open's upwards.

Thus, a = 1/(4·2) = 8, vertex at (7,0).

This means that :

y = (x-7)2/8

over the argument its not good to fight.

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4