Question

Find the coordinates of the focus, the axis of the parabola, the equation of directrix, and the length of the latus rectum for $y^2 = 12x$.

Answer 1

The given equation is $y^2= 12x.$
Here, the coefficient of $x$ is positive.
Hence, the parabola opens towards the right.
On comparing this equation with $y^2 = 4ax$ , we obtain
$4a= 12$
$⇒ a = 3$$$

∴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., $x = - 3$

$⇒ x+ 3 = 0$
Length of latus rectum : $4a= 4*3$ $=12$$$ (Ans.)