Question

Which is the standard form of the equation of a parabola with a focus of (8, 0) and directrix x = –8?

Answer 1

Focus (8,0) and directrix x = −8 have vertex at midpoint (0,0). The axis is horizontal and p = 8, so the standard form is

y^2 = 4px = 4·8·x = 32x.

(Equivalently, from distance equality √[(x−8)^2 + y^2] = |x+8|, squaring gives y^2 = 32x.)