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 :

Step-by-step solution

Given, The line y = - x bisect the chord P Q If λ , - λ is the mid-point of the chord P Q then, Q ( 2 λ - α , - 2 λ - β ) Given circle 2 x 2 + 2 y 2 - ( 1 + a ) x - ( 1 - a ) y = 0 Or, x 2 + y 2 - 1 + a 2 x - 1 - a 2 y = 0 Let 1 + a 2 = α , 1 - a 2 = β The circle equation will be, x 2 + y 2 - α x - β y = 0 Point Q will lie on the circle, ( 2 λ - α ) 2 + ( - 2 λ - β ) 2 - α ( 2 λ - α ) - β ( - 2 λ - β ) = 0 ⇒ 4