Question

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

Answer 1

Here is your answer.

Answer 2

Given O (2,3) is the center of the circle .

(Diagram in attachment)

Given points are A(4,3) and B(x,5)

Using distance formula,

√(2-4)^2 + (3-3)^2 = √(x-2)^2 + (5-3)^2

√(-2)^2 + (0) = √ x^2 - 4x + 4 + (2)^2

√4 = √x^2 - 4x +4 + 4

Squaring both sides,

4 = x^2 - 4x + 8

x^2 - 4x + 8 - 4 = 0

x^2 - 4x + 4 = 0

x^2 - 2x - 2x + 4 = 0

x( x - 2 ) - 2( x - 2 ) = 0

( x - 2 ) ( x - 2) = 0

x - 2 = 0

x = 2