The equation of the circle whose diameter is the common chord of the circles x^2+y^2+2 x+2 y+1=0 and x^2+y^2+4 x+6 y+4=0 is

Step-by-step solution

Given, S₁ x^2+y^2+2 x+2 y+1=0 and S₂ x^2+y^2+4 x+6 y+4=0 Now, the equation of common chord of these two circles. S₁-S₂=0 aligned & (x^2+y^2+2 x+2 y+1 )- & (x^2+y^2+4 x+6 y+4 )=0 & -2 x-4 y-3=0 i.e. 2 x+4 y+3=0 aligned The equation of required circle, aligned & S₁+ (S₂-S₁ )= & (x^2+y^2+2 x+2 y+1 )+ (2 x+4 y+3)=0 & x^2+y^2+2 x(1+ )+2 y(2 +1)+3 +1=0 aligned Diameter of the above circle is the common chord of circles S₁ and S₂ . So, 2(-(1+ ))+4(-(2 +1))+3=0 -2-2 -8 -4+3=0 10 =-3 = -3 10 Hence, the required circle align