Class 11

Math

3D Geometry

Conic Sections

Find the equation of the parabola that satisfies the following conditions: Focus $(0,−3)$; directrix $y=3$

Since, the focus lies on the $y$-axis and directrix $y=3$ is above the $x$-axis.

So, the axis of the parabola is $y$-axis.

Therefore, the equation of the parabola is either of the form $x_{2}=−4ay$

Here $a=3$

Thus, the equation of the parabola is $x_{2} =−12y$