Find the equation of a circle which passes through the point (1,2) and the points of intersection of the circles x^2+y^2-8 x-6 y+21=0 and x^2+y^2-2 x-15=0

Step-by-step solution

gathered C₁: x^2+y^2-8 x-6 y+21=0 C₂: x^2+y^2-2 x-15=0 gathered Equation of circle passing through the point of intersection. gathered S₁+ S₂=0 (x^2+y^2-8 x-6 y+21 )+s (x^2+y^2-2 x-15 )=0 gathered Now, equation of circle passing through (1,2) is aligned & (1^2+2^2-8(1)-6(2)+21 ) & .+ 1(1)^2+(2)^2-2(1)-15 ) =0 & (1+4-8-12+21)+ (5-2-15)=0 & 6+ (-12)=0 = 1 2 aligned Equation of required circle is aligned & (x^2+y^2-8 x-6 y+21 )+ 1 2 (x^2+y^2-2 x-15 )=0 & 3 x^2+3 y^2-18 x-12 y+42-15=0 & 3 (x^2+y^2-6 x-4 y+9 )=0 & x^2+y