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.
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
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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