Find the intervals of the values of 'a' for which the line bisects two chords drawn…

MATHEMATICS · Subjective · CBSE · Mathematics · Conic Sections · Conic Sections

Problem

Find the intervals of the values of 'a' for which the line y+x=0y + x = 0 bisects two chords drawn from a point (1+2a2,1−2a2)\left( \frac{1 + \sqrt{2}a}{2}, \frac{1 - \sqrt{2}a}{2} \right) to the circle 2x2+2y2−(1+2a)x−(1−2a)y=0.2x^2 + 2y^2 - (1 + \sqrt{2}a)x - (1 - \sqrt{2}a)y = 0.

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