Question:
Find the coordinates of the focus, axis of the parabola, the equation of directrix and the length of the latus rectum for $y^{2}=-8 x$
Solution:
The given equation is $y^{2}=-8 x$.
Here, the coefficient of $x$ is negative. Hence, the parabola opens towards the left.
On comparing this equation with $y^{2}=-4 a x$, we obtain
$-4 a=-8 \Rightarrow a=2$
$\therefore$ 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., $x=2$
Length of latus rectum $=4 a=8$