Question

Find the equation of the parabola with vertex at the origin and focus at $f(-2,0)$

Answer 1

Solve for the equation of parabola

It is given that focus of parabola is $(-2,0)$ and vertex is $\left(0,0\right)$

General equation of parabola with focus$(a,0)$ and vertex at origin is $y^2=4ax$

Now substitute the value of $a=-2$

$\Rightarrow y^2=4(-2)x$

$\Rightarrow y^2$ $=-8x$

Hence the required equation of parabola with vertex at the origin and focus at$(-2,0)$ is $y^2=-8x$