Centre of circle whose normals are x2−2xy−3x+6y=0, is
x2–2xy–3x+6y=0x2–2xy–3x+6y=0
x(x–3)–2y(x–3)=0x(x–3)–2y(x–3)=0
(x–2y)(x–3)=0(x–2y)(x–3)=0
x−2y=0x−2y=0 are the normal equations.
WKT normal passes through center intersection of two normal will give center
x=3,x=2y
y=3/2
Center is (3,3/2)