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

Since the line passing through the focus and perpendicular to the directrix is x-axis. Therefore, axis of the required parabola is x-axis. Let the coordinates of the focus $S$ be

Since the vertex is the mid point of the line joining the focus and the point (- 5, 0) where the directrix x + 5 = 0 meets the axis.

$\therefore -3=\frac{a-5}{2}\Rightarrow a=-1$

Thus, the coordinates of the focus are (-1, 0). Let $P (x, y)$ be a point on the parabola. Then, by definition, we have

$\sqrt{(x+1{)}^2+y^2}=(x+5{)}^2\Rightarrow y^2=8(x+3)$