The set of all values of a 2 for which the line x + y = 0 bisects two distinct chords drawn from a point P ( 1 + a 2 , 1 - a 2 ) on the circle 2 x 2 + 2 y 2 - ( 1 + a ) x - ( 1 - a ) y = 0 , is equal to [2023]

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Solution

Q.
The set of all values of $a^{2}$ for which the line $x + y = 0$ bisects two distinct chords drawn from a point $P (\frac{1 + a}{2}, \frac{1 - a}{2})$ on the circle $2 x^{2} + 2 y^{2} - (1 + a) x - (1 - a) y = 0,$ is equal to [2023]

1 $(8, \infty)$

2 $(0, 4]$

3 $(4, \infty)$

4 $(2, 12]$

Ans.
(1)

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