LetS:x2+y2+2gx+2fy+c=0 ∵ The power of the point(2,0)with respect to circleSis -4 ‌∴(2)2+(0)2+2g(2)+2f(0)+c=−4 ‌⇒‌‌4g+c+8=0‌‌...‌ (i) ‌ ∵ The length of tangent drawn from the point(1,1)to S is 2 ∴‌√(1)2+(l)2+2g(l)+2f(l)+c=2 ⇒2g+2f+c+2=4 ⇒2g+2f+c−2=0‌‌...‌ (ii) ‌ ∵ The circle S is passing through(−1,−1). ‌∴(−1)2+(−1)2+2g(−1)+2f(−1)+c=0 ‌⇒‌‌−2g−2f+c+2=0 ‌⇒‌‌2g+2f−c−2=0...‌ (iii) ‌ On solving Eqs. (i), (ii) and (iii), we get g=−2f=3andc=0 ∴‌‌S=x2+y2−4x+6y=0 Radius of S=√g2+f2−c ‌=√(−2)2+(3)2−0 ‌=√4+9=√13
