Question

How do you find the equation of a parabola with vertex at the origin and focus (-2,0)?

Answer 1

`y^2=-8x`

Explanation:

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

We have axis of symmetry as `y=0` and directrix as `x=2`.

As parabola is the locus of a point equidistant from focus `(-2,0)` and directrix `x=2`, hence the equation of parabola is

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

or `y^2=-8x`

graph{(y^2+8x)((x+2)^2+y^2-0.02)(x-2)=0 [-10, 10, -5, 5]}