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Find the coordinates of the focus, axis of the parabola, the equation of the directrix and the length of the latus rectum. x to the power 2 equals minus 9y

6. Find the coordinates of the focus, axis of the parabola, the equation of the directrix and the length of the latus rectum.

       x^2 = -9y

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Given, a parabola with equation 

x^2 =-9y

This is parabola of the form x^2=-4ay which opens downwards.

So

By comparing the given parabola equation with the standard equation, we get,

-4a=-9

a=\frac{9}{4}

Hence,

Coordinates of the focus :

(0,-a)=\left (0,-\frac{9}{4}\right)

Axis of the parabola:

It can be seen that the axis of this parabola is Y-Axis.

The equation of the directrix

y=a,\Rightarrow y=\frac{9}{4}\Rightarrow y-\frac{9}{4}=0

The length of the latus rectum:

4a=4\left(\frac{9}{4}\right)=9.

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