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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. y ^2 = 12 x

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

       y^2 =12x

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Given, a parabola with equation 

y^2 =12x

This is parabola of the form y^2=4ax which opens towards the right.

So,

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

4a=12

a=3

Hence,

Coordinates of the focus :

(a,0)=(3,0)

Axis of the parabola:

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

The equation of the directrix

x=-a,\Rightarrow x=-3\Rightarrow x+3=0

The length of the latus rectum:

4a=4(3)=12.

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