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Question

Find the coordinates of the focus, axis of the parabola, the equation of directrix and the length of the rectum for y2=12x

Solution
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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 obtain
4a=12a=3
Coordinates of the focus =(a,0)=(3,0)
Since the given equation involves y2 the axis of the parabola is the x-axis
Equation of direcctrix x=ai.e.,x=3i.e.,x+3=0
Length of latus rectum =4a=4×3=12

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