The equation of the circle whose diameter is common chord to the circles x²+y²+2 a x+c=0 and x²+y²+2 b y+c=0 is

Step-by-step solution

Let S₁ x²+y²+2 a x+c=0 and S₂ x²+y²+2 b y+c=0 Equation of common chord as a diameter of the third circle aligned S₁-S₂ &=0 a x-b y &=0 y &= a x b ...(i) aligned On putting the value of y in Eq. (i), we get array r x²+ ( a² x² b² )+2 a x+c=0 (a²+b² ) x²+2 a b² x+c b²=0 array Let x₁ and x₂ be the roots of the equation. x₁+x₂= -2 a b² a²+b² and x₁ x₂= c b² a²+b² Similarly, (a²+b² ) y²+2 b a² y+c a²=0 Let y₁ and y₂ be the roots of the equation y₁+y₂= -2 a² b a²+b² and y₁ y₂= c a² a²+b² Now, the required equation of thi