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$$=-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 $y^2=-4ax$
$-4a=-8$
$\Rightarrow a=2$
$\therefore$ Coordinates of the focus $=(-a,0)=(-2,0)$
Axis of the parabola is the $x$-axis i.e.$y=0$
Equation of directrix $x=a$ i.e.,$x=2$
Length of latus rectum $=4a=8$