Q. 14.4( 81 Votes )

# In each of the following, 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

Answer :

The given equation is y^{2} = 12x

Here, the coefficient of x is positive.

Hence, the parabola opens towards the right.

On comparing this equation with y^{2} = 4ax, we get,

4a = 12

⇒ a = 3

Thus,

Co-ordinates of the focus = (a, 0) = (3, 0)

Since, the given equation involves y^{2}, the axis of the parabola is the x-axis.

Equation of directrix, x =-a, then,

x + 3 = 0

Length of latus rectum = 4a = 4 × 3 = 12

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