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# Find the equation of the parabola that satisfies the given conditions: Focus $(0,-3)$ and Directrix $y=3$

$\begin{array}{1 1}x^2 = -12y \\ x^2 = 12y \\ y^2 = -12x \\ y^2 = 12x \end{array}$

Given Focus $(0,-3)$ and Directrix $y=3$
Since the Focus is on the y-axis $\rightarrow$ this is the axis of the parabola.
The Directrix $y=3$ is above the x-axis while the focus is below the x-axis. Therefore the parabola is of the form $x^2=-4ay$
Therefore, this is of the type $x^2 = -4ay \rightarrow a = 3$
Therefore the equation of the parabola is $x^2 = - 4 \times 3 y = -12 y$
edited Apr 11, 2016 by meena.p