EF = perpendicular bisector of chord AB

BG = perpendicular to y-axis

Here C = center of the circle

mid-point of chord AB, D = ($$-$$ 1, 3)

slope of AB = $${{4 - 2} \over { - 2 - 0}}$$ = $$-$$ 1

$$ \because $$   EF  $$ \bot $$ AB

$$ \therefore $$   Slope of EF = 1

Equation of EF, y $$-$$ 3 = 1 (x + 1)

$$ \Rightarrow $$    y = x + 4       . . . .(i)

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 center, C = ($$-$$ 2, 2)

Now coordinates of center C satiesfy the equation

2x $$-$$ 3y + 10 = 0

Hence 2x $$-$$ 3y + 10 = 0   is the equation of the diameter