jee-main 2023 Q68

jee-main · India · session1_31jan_shift2 Circles Chord Length and Chord Properties

The set of all values of $a^2$ for which the line $x + y = 0$ bisects two distinct chords drawn from a point $\mathrm{P}\left(\frac{1+a}{2}, \frac{1-a}{2}\right)$ on the circle $2x^2 + 2y^2 - (1+a)x - (1-a)y = 0$, is equal to:
(1) $(8, \infty)$
(2) $(0, 4]$
(3) $(4, \infty)$
(4) $(2, 12]$

The set of all values of $a^2$ for which the line $x + y = 0$ bisects two distinct chords drawn from a point $\mathrm{P}\left(\frac{1+a}{2}, \frac{1-a}{2}\right)$ on the circle $2x^2 + 2y^2 - (1+a)x - (1-a)y = 0$, is equal to:\\
(1) $(8, \infty)$\\
(2) $(0, 4]$\\
(3) $(4, \infty)$\\
(4) $(2, 12]$

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