Given diameters' equation: y + 2x - 3 = 0 ...(i) 2y + 3x - 2 = 0 ...(ii) Substracting (ii) from 2 × (i) x - 4 = 0 ⇒ x = 4 From equation (i) y + 2(4) - 3 = 0 ⇒ y + 5 = 0 ⇒ y = -5 ∴ Coordinates of the centre are (4, -5) Given the circle passes through (2, 2) Now the radius r=√(y2−y1)2+(x2−x1)2 ⇒r=√(−5−2)2+(4−2)2 ⇒r=√49+4 ⇒r2=53 ∴ The equation of circle is: (x−h)2+(y−k)2=R2 ⇒(x−4)2+(y+5)2=53 ⇒x2+y2−8x+10y+16+25=53 ⇒x2+y2−8x+10y−12=0