Find the coordinates of the focus, axis of the parabola, the equation of the directrix and the length of the latus rectum x2 = – 9y

Asked by Pragya Singh | 11 months ago |  106

##### Solution :-

The equation is x2 = -9y

Here we know that the coefficient of y is negative.

So, the parabola open downwards.

On comparing this equation with x2 = -4ay, we get,

-4a = -9

a = $$\dfrac{-9}{-4}$$$$\dfrac{9}{4}$$

Thus, co-ordinates of the focus = (0,-a)

= (0, $$\dfrac{-9}{4}$$)

Since, the given equation involves x2, the axis of the parabola is the y-axis.

The equation of directrix, y = a, then,

y = $$\dfrac{9}{4}$$

Length of latus rectum = 4a

= 4($$\dfrac{9}{4}$$) = 9

Answered by Abhisek | 11 months ago

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