Question

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

Answer 1

Vertex $A(0,0)$; focus $S(-2,0)$
Since, the vertex of the parabola is $0,0)$and the focus lies on the negative $x$-axis . So, $x$-axis is the axis of the parabola .
Equation of the parabola is of the form $y^2=-4ax$
Since, the focus is $(-2,0)$. So, $a=2$
Thus, the equation of the parabola is $y^2=-8x$