Class 11

Math

3D Geometry

Conic Sections

Find the coordinates of the focus, axis of the parabola, the equation of directrix and the length of the rectum for $y_{2}=12x$

Here the coefficient of $x$ is positive.

Hence the parabola opens right

On comparing this equation with $y_{2}=4ax$,

$4a=12$

$⇒a=3$

$∴$ 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 directrix $x=−a$ i.e. $x=−3$

Length of latus rectum $=4a=12$