Find the coordinates of the focus, axis of the parabola, the equation of the directrix and the length of the latus rectum x2 = – 16y

Asked by Pragya Singh | 1 year ago |  93

##### Solution :-

The equation is x2 = -16y

Here we know that the coefficient of y is negative.

So, the parabola opens downwards.

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

-4a = -16

a =$$\dfrac{-16}{-4}$$

= 4

Thus, co-ordinates of the focus = (0,-a) = (0,-4)

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

The equation of directrix, y =a, then,

y = 4

Length of latus rectum = 4a = 4(4) = 16

Answered by Abhisek | 1 year ago

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