EF= perpendicular bisector of chord AB BG= perpendicular to y -axis Here C= centre of the circle mid-point of chord AB,D=(−1,3) slope of AB=
4−2
−2−0
=−1 ∵EF⟂AB ∴ Slope of EF=1 Equation of EF,y−3=1(x+1) . . . (i) ⇒y=x+4 Equation of BG y=2 . . . (ii) From equations (i) and (ii) x=−2,y=2 since C be the point of intersection of EF and BG, therefore centre, C=(−2,2) Now coordinates of centre C satisfy the equation 2x−3y+10=0 Hence 2x−3y+10=0 is the equation of the diameter