The set of all values of … for which the line … bisects two distinct chords drawn from a point … on the circle …, is equal to :

Circle

JEE Main 2023 · 31 Jan, Evening shift · Q3054

MathematicsHard127×since 2002Q3054

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

2 x^{2}+2 y^{2}-(1+a) x-(1-a) y=0

, is equal to :

JEE Main 2023 · 31 Jan, Evening shift · Q3054

MathematicsHard127×since 2002Q3054

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

2 x^{2}+2 y^{2}-(1+a) x-(1-a) y=0

, is equal to :