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:
$y^{2}=12 x$
Solution:
Given equation : $y^{2}=12 x$
Comparing given equation with parabola having equation,
$y^{2}=4 a x$
$4 a=12$
- $a=3$
Focus :
$F(a, 0)=F(3,0)$
Vertex :
$\mathrm{A}(0,0)=\mathrm{A}(0,0)$
Equation of the directrix : x+a=0
- $x+3=0$
$x=-3$
Lenth of latusrectum : $4 \mathrm{a}=4 .(3)=12$
