Question

Find the equation of parabola whose focus is `(-2,0)` and vertex is `(0,0)`?

Answer 1

`y^2=-4x`

Explanation:

As focus is `(-2,0)` and vertex is `(0,0)`,

axis of symmetry is `y=0`

and as vertex is midway between focus and directrix and directrix is perpendicular to axis of symmetry

directrix is `x=2`

Now as parabola is the locus of point which moves so that it is equidistant from focus and directrix, hence equation is

`(x+2)^2+y^2=(x-2)^2`

or `y^2=(x-2)^2-(x+2)^2=-4x`

graph{(y^2+4x)((x+2)^2+y^2-0.03)(x^2+y^2-0.03)(x-2)=0 [-10, 10, -5, 5]}