Question

If the points a(4,3) and b(x,5) are on the circle with centre o(2,3), then find the value of x2 + 5.

Answer 1

A(4,3) B(x,5) O(2,3)

OA = OB {radius of circle}

OA square = OB square

Using distance formula

(2 - 4)square + (3 - 3)square = (2 - x) square +(3 - 5)square

4 + 0 = 4 + x square - 4x + 4

0 = x square - 4x + 4

Using middle term splitting

x square - 2x - 2x + 4 = 0

x = 2

x square + 5

= 2 square + 5

= 9