Question

How do you find the vertex, focus and directrix of `-48x = y^2`?

Answer 1

(1) the Vertex is, `(0,0)`.

(2) Focus is `(a,0)=(-12,0)`, and,

(3) Eqn. of Directrix is `: x+a=0, i.e., x=12`.

Explanation:

Comparing with the Standard Eqn. `y^2=4ax, a=-12`.

Hence, (1) the Vertex is, `(0,0)`.

(2) Focus is `(a,0)=(-12,0)`, and,

(3) Eqn. of Directrix is `: x+a=0, i.e., x=12`. graph{y^2=-48x [-118.6, 118.55, -59.2, 59.3]}