Question

Find the coordinates of the focus, axis of the parabola, the equation of directrix and the length of the 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
$4a=12\Rightarrow a=3$
$\therefore$ 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 $x=-ai.e.,x=-3i.e.,x+3=0$
Length of latus rectum $=4a=4\times 3=12$