The vertex and endpoints of the latus rectum of a parabola are given. Find the equation of the parabola. V(0, 0), endpoints (−3, 6), (−3, −6)

Answer 1

It's a leftward opening parabola of the general form x=-a(y-h)^2 + k where (k,h) is the vertex. with the vertex at the origin, it becomes x=-ay^2

plug in either point to solve for a

-3 = -a(6)^2 = -36a

a = 3/36 = 1/12

x=-(1/12)y^2 is the parabola equation.