Find the coordinates of the focus and the vertex, the equations of the
Question:

Find the coordinates of the focus and the vertex, the equations of the directrix and the axis, and length of the latus rectum of the parabola :

$y^{2}=-8 x$

Solution:

Given equation :

$y^{2}=-8 x$

Comparing given equation with parabola having equation,

$y^{2}=-4 a x$

$4 a=8$

– $a=2$

Focus: $F(-a, 0)=F(-2,0)$

Vertex: $A(0,0)=A(0,0)$

Equation of the directrix: $x-a=0$

$\cdot x-2=0$

$\cdot x=2$

Lenth of latusrectum : $4 \mathrm{a}=8$