Question:
Find the coordinates of the focus, axis of the parabola, the equation of directrix and the length of the latus rectum for $y^{2}=12 x$
Solution:
The given equation is $y^{2}=12 x$.
Here, the coefficient of x is positive. Hence, the parabola opens towards the right.
On comparing this equation with $y^{2}=4 a x$, we obtain
$4 a=12 \Rightarrow a=3$
$\therefore$ Coordinates of the focus $=(a, 0)=(3,0)$
Since the given equation involves $y^{2}$, the axis of the parabola is the $x$-axis.
Equation of direcctrix, $x=-a$ i.e., $x=-3$ i.e., $x+3=0$
Length of latus rectum $=4 a=4 \times 3=12$