Question

Find the vertex, focus, and directrix of the parabola.3x2 + 16y

Answer 1

i assume you mean 3x^2 + 16y = 0

so y = -3/16 x^2

The vertex is at the origin (0,0) answer

x^2 = -16/3 y

compare with standard form x^2 = 4ay:-

the focus y coordinate of the a = -16/3 / 4

= -16/12 = -4/3 so the focus is (0, -4/3) answer

and the directrix is y = 4/3 answer