The end points of latus rectum of the parabola $x^{2} = 4 a y$ are

(a, 2a), (2a, - a)

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(-a, 2a), (2a, a)

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(a, -2a), (2a, a)

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(-2a, a) ,(2a, a)

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Solution

The correct option is D (-2a, a) ,(2a, a)
Latus rectum is the chord which passes through the focus and is perpendicular to the axis. Focus of the given parabola is (0,a) and the axis is y-axis or the line x=0. Now the equation of the line which passes through (0,a) and perpendicular to y-axis is y = a. The points where this line intersects the parabola is the end points of parabola.
=> (2a, a) and (-2a,a) are the end points.

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