Question

Which is the standard form of the equation of the parabola that has a vertex of (3, 1) and a directrix of x = –2?

Answer 1

The parabola opens right since the directrix x = -2 is left of the vertex (3,1). For a horizontal parabola with vertex (h,k),

(y − k)^2 = 4p(x − h).

Here h = 3 and h − p = −2, so p = 5. Thus

(y − 1)^2 = 20(x − 3).