If and are two focal chords of the parabola at right angles

MATHEMATICS · Multi correct · CBSE · Mathematics · Conic Sections · Conic Sections

Problem

If P1P2P_1P_2 and Q1Q2Q_1Q_2 are two focal chords of the parabola y2=4axy^2=4ax at right angles, then (1) The area of the quadrilateral P1Q1P2Q2P_1Q_1P_2Q_2 is minimum when the chords are inclined at an angle π4\frac{\pi}{4} to the axis of the parabola. (2) The minimum area is twice the area of the square on the latus rectum of the parabola. (3) The minimum area of quadrilateral P1Q1P2Q2P_1Q_1P_2Q_2 cannot be found. (4) The minimum area is thrice the area of the square on the latus rectum of the parabola.

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