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 : $4 \mathrm{a}=8$
