Question

If the vertex of a parabola is the point $(-3,0)$ and the directrix is the line $x+5=0$, then find its equation.

Answer 1

Given the vertex of the parabola is $(-3,0)$

The equation of directrix is $x+5=0$

Equation of the parabola is $(y-0{)}^2=4a(x-\left(3\right))$

$y^2=4a(x+3)$

$x=-a$ is the equation of directrix

Given directrix is $x+5$

i.e., $x+5-3=0$

$x+2=0$

$a=2$

Equation of required parabola is $y^2=8(x+3)$.