The circles a x^ 2 +a y^ 2 +2 g_ 1 x+2 f_ 1 y+c_ 1 =0 and b x^ 2 +b y^ 2 +2 g_ 2 x+2 f_ 2…
Mathematics · JEE Main · NTA Exams — Co-ordinate Geometry
The circles \(a x^{2}+a y^{2}+2 g_{1} x+2 f_{1} y+c_{1}=0\) and \(b x^{2}+b y^{2}+2 g_{2} x+2 f_{2} y+c_{2}=0\) \((a \neq 0 \text { and } b \neq 0)\) cut orthogonally if
- \(g_{1} g_{2}+f_{1} f_{2}=a c_{1}+b c_{2}\)
- \(Z\left(g_{1} g_{2}+f_{1} f_{2}\right)=b c_{1}+a c_{2}\)
- \(b g_{1} g_{2}+a f_{1} f_{2}=b c_{1}+a c_{2}\)
- \(g_{1} g_{2}+f_{1} f_{2}=c_{1}+c_{2}\)
Answer
(C) b g_ 1 g_ 2 +a f_ 1 f_ 2 =b c_ 1 +a c_ 2
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