The equation of the circle passing through the origin and the points of intersection of the circles x2+y2−4x−6y−3=0, x2+y2+4x−2y−4=0
By family of circles,
equation of circle passing through point of
intersection
of s1:x2+y2−4x−6y−3=0
and s2:x2+y2+4x−2y−4=0 is
∴s1+λs2=0
⇒(1+λ)x2+(1+λ)y2+4(λ−1)x−2(3+λ)y−3−4λ=0
Given this circles pass through origin (0,0)
∴−3−4λ=0
λ=−34
∴ Equation of circle is
x24+y24−28x4−18y4=0
⇒x2+y2−28x−18y=0