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 latus rectum for $x_{2}=−9y$

Here the coefficient of $y$ is negative.

Hence, the parabola opens downwards

On comparing this equation with $x_{2}=−4ay$, we get

$−4a=−9$

$⇒a=49 $

$∴$ Coordinates of the focus $=(0,−a)=(0,−49 )$

Axis of the parabola is the $y$-axis i.e $x=0$

Equation of directrix $y=a$ i.e. $y=49 $

Length of latus rectum $=4a=9$