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.

y2 = 12x

The given equation is y2 = 12x


Here, the coefficient of x is positive.


Hence, the parabola opens towards the right.


On comparing this equation with y2 = 4ax, we get,


4a = 12


⇒ a = 3


Thus,


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


Since, the given equation involves y2, 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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