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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 = 6y

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

       x^2 = 6y

Answers (1)

best_answer

Given, a parabola with equation 

x^2 =6y

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

So,

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

4a=6

a=\frac{3}{2}

Hence,

Coordinates of the focus :

(0,a)=\left (0,\frac{3}{2}\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{3}{2}\Rightarrow y+\frac{3}{2}=0

The length of the latus rectum:

4a=4(\frac{3}{2})=6.

Posted by

Pankaj Sanodiya

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