Q. 124.7( 4 Votes )

# If the points A(4, 3) and B(x, 5) lie on the circle with centre 0(2, 3), find the value of x.

Answer :

The distance of any point which lies on the circumference of the circle from the centre of the circle is called radius.

∴ OA = OB = Radius of given Circle

taking square on both sides, we get-

OA^{2} = OB^{2}

⇒ (2-4)^{2} + (3-3)^{2} = (2-x)^{2} + (3-5)^{2}

[using distance formula, the distance between points (x_{1},y_{1}) and (x_{2},y_{2}) is equal to units.]

⇒ (-2)^{2} + 0 = x^{2}-4x + 4 + (-2)^{2}

⇒ x^{2}-4x + 4 = 0

⇒ (x-2)^{2} = 0

∴ x = 2

Thus, the value of x is 2.

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