Find the coordinates of the focus, axis of the parabola, the equation of the directrix and the length of the latus rectum.x2 = 6y

Asked by Pragya Singh | 11 months ago |  80

1 Answer

Solution :-

The equation is x2 = 6y

Here we know that the coefficient of y is positive.

So, the parabola opens upwards.

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

4a = 6

a = \( \dfrac{6}{4}\)

\( \dfrac{3}{2}\)

Thus, the co-ordinates of the focus = (0,a) = (0,\( \dfrac{3}{2}\))

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

The equation of directrix, y =-a, then,

y = \( \dfrac{-3}{2}\)

Length of latus rectum = 4a 

= 4(\( \dfrac{3}{2}\)) = 6

Answered by Abhisek | 11 months ago

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