# Find the coordinates of the focus, axis of the parabola,

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 $=4 a=8$