Question

Find the coordinates of the focus, the axis of the parabola, the equation of directrix, and the length of the latus rectum for $y^2 = - 8x$

Answer 1

The given equation is $y^2= -8x$.
Here, the coefficient of x is negative. Hence, the parabola opens towards the left.
On comparing this equation with $y^2= -4ax,$ we obtain
$-4a= -8$

$⇒ a = 2$

∴Coordinates of the focus = $(-a, 0) = (-2, 0)$ Since the given equation involves $y^2$, the axis of the parabola is the x-axis.
Equation of directrix, $x= a$

i.e.$,x = 2$

The length of the latus rectum is $4a= 8$ (Ans.)