The circles a x²+a y²+2 g₁ x+2 f₁ y+c₁=0 and b x²+b y²+2 g₂ x+2 f₂ y+c₂=0(a 0 and b 0) cut orthogonally if

Step-by-step solution

Given equation of circles are a x²+a y²+2 g₁ x+2 f₁ y+c₁=0 and b x²+b y²+2 g₂ x+2 f₂ y+c₂=0 It can be rewritten as, x²+y²+ 2 g₁ a x+ 2 f₁ a y+ c₁ a =0 and x²+y²+ 2 g₂ b x+ 2 f₂ b y+ c₂ b =0 So, centres of circle (- g₁ a ,- f₁ a ) and (- g₂ b ,- f₂ b ) respectively. We know that, if two circles cut orthogonally, then aligned & 2 (g₁ g_ z +f_ i f_ 2 )=c_ i +c_ z & 2 ( g ₁ g₂ a b + f₁ f₂ a b )= c₁ a + c₂ b & 2 (g₁ g₂+f₁ f₂ )=b c₁+a c₂ aligned