Question

Find the equation of the parabola with vertex $(0,0)$ and focus at $(-\frac{1}{2},0)$

Answer 1

Since the focus of the parabola is $F(-\frac{1}{2},0)$ which lies on $x-$axis itself is the axis of the parabola.

Also, the vertex of the parabola is at $O(0,0)\therefore ,$ the parabola is of the form $y^2=-4ax$ with $a=\frac{1}{2}$

Hence the required equation of the parabola is $y^2=-4\times \frac{1}{2}x=-2x$