pointA(-1,y) and B(5,7) lie on the circle with centre O(2,-3y).Find the values of y.Hence findd the radius of the circle

OA=OB → Find the value of y from this eqn using distance formula for both OA and OB. After solving for y, Find either OA or OB to be the radius of the circle.

Given, Centre of the circle is O (2, 3).A (4, 3) and B (x, 5) are two points on the circle.∴ OA = OB (Radius of the circle)Squaring on both sides, we get∴ 4 + 0 = (x – 2)2 + 4⇒ (x – 2)2 = 0⇒ x – 2 = 0⇒ x = 2Thus, the value of x is 2.