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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 ^ 2 = - 16 y

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

   x^2 = -16y

Answers (1)

best_answer

Given, a parabola with equation 

x^2 =-16y

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=-16

a=4

Hence,

Coordinates of the focus :

(0,-a)=(0,-4)

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=4\Rightarrow y-4=0

The length of the latus rectum:

4a=4(4)=16.

Posted by

Pankaj Sanodiya

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