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Find the equation of the parabola that satisfies the given conditions: Focus (0, - 3); directrix y = 3

8. Find the equation of the parabola that satisfies the given conditions:

     Focus (0,–3); directrix y = 3

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Given,in a parabola,

Focus : Focus (0,–3); directrix y = 3

Here,

Focus is of the form (0,-a), which means it lies on the Y-axis. And Directrix is of the form y=a which means it lies above X-Axis.

These are the conditions when the standard equation of a parabola is  x^2=-4ay.

Hence the Equation of Parabola is

 x^2=-4ay

Here, it can be seen that:

a=3

Hence the Equation of the Parabola is:

\Rightarrow x^2=-4ay\Rightarrow x^2=-4(3)y

\Rightarrow x^2=-12y.

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