Question

Find the equation of the parabola that satisfies the following conditions: Vertex $(0, 0)$ focus $(-2, 0)$

Answer 1

Vertex $(0, 0)$focus $(-2, 0)$
Since the vertex of the parabola is $(0, 0)$ and the focus lies on the negative x-axis, the x-axis is the axis of the parabola, while the equation of the parabola is of the form $y^2= -4ax.$
Since the focus is $(-2, 0)$, $a= 2.$
Thus, the equation of the parabola is $y ^2= -4*2x$

,i.e., $y^2= -8x$ (Ans.)