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If the focus of a parabola is $(0,-3)$ and its directrix is $y=3$, then its equation is
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Verified Answer
The correct answer is:
$x^2=-12 y$
$x^2=-12 y$
Since, focus of parabola is $(0,-3)$ and its directrix is $y=3$.
Now, by definition of parabola,
$$
\begin{aligned}
&\sqrt{(x-0)^2+(y+3)^2}=|y-3| \\
&\Rightarrow x^2+y^2+6 y+9=y^2-6 y+9 \\
&\Rightarrow x^2+12 y=0 \Rightarrow x^2=-12 y
\end{aligned}
$$
Now, by definition of parabola,
$$
\begin{aligned}
&\sqrt{(x-0)^2+(y+3)^2}=|y-3| \\
&\Rightarrow x^2+y^2+6 y+9=y^2-6 y+9 \\
&\Rightarrow x^2+12 y=0 \Rightarrow x^2=-12 y
\end{aligned}
$$
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