Question

The end points of latus rectum of the parabola $x^2=4ay$ are

• A. (a, 2a), (2a, - a)
• B. (-a, 2a), (2a, a)
• C. (a, -2a), (2a, a)
• D. (-2a, a) (2a, a)

Answer 1

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.