Question

what is the equation of a parabola with a directrix x = 8 and focus (-8,0)

Answer 1

From the given information, the parabola is a sideways parabola facing left with vertex at the origin.
Required equation is (y - 0)^2 = 4p(x - 0)
y^2 = 4px

But 0 + p = -8 => p = -8

Therefore, required equation is y^2 = 4(-8)x
y^2 = -32x