Circle passes through (1,λ), then the equation of circle be (1−h)2+(λ−k)2=r2 ⇒ h2+k2−2h−2λk+λ2+1=r2 .......(i) Circle passes through (λ,1),then the equation of circle be (λ−h)2+(1−k)2=r2 ⇒ h2+k2−2hλ−2k+λ2+1=r2 .......(ii) Circle passes through (λ,λ), then the equation of circle be (λ−h)2+(λ−k)2=r2 ⇒ h2+r2−2λh−2λk+2λ2=r2 .......(iii) On subtracting eq. (ii) from (i), we get 2hλ−2h+2k−2λk=0 ⇒ (λ−1)h−(λ−1)k=0 ⇒ (λ−1)(h−k)=0 h=k[∴λ≠1] On subtracting eq. (iii) from (ii), we get 2λk−2k−λ2+1=0 ⇒ k=λ2−