Circles Part 1

The given circles are
S1≡x2+y2+3x+7y+2p−5=0.....(1)
S2≡x2+y2+2x+2y−p2=0.....(2)
∴ Equation of common chord PQ is S1−S2=0
⇒L≡x+5y+p2+2p−5=0
⇒ Equation of circle passing through P and Q is
S1+λL=0
⇒(x2+y2+3x+7y+2p−5)+λ
(x+5y+p2+2p−5)=0
As it passes through (1,1), therefore
‌⇒(7+2p)+λ(2p+p2+1)=0
‌⇒λ=−‌

2p+7

(p+1)

which does not exist for p=−1