Question

Find the equation of the parabola that satisfies the given conditons:

Vertex (0,0) and Focus (-2,0)

Answer 1

The vertex of the parabola is at (0,0) and focus is at (-2,0).
$\therefore y=0\Rightarrow$ The axis of parabola is along x - axis
So the parabola is of the form $y^2=4ax.$
The required equation of parabola is,
$y^2=4\times -2x\Rightarrow y^2=-8x$