Question

The centre of a circle passing through P(8, 5) is (x+l , x-4). Find the coordinates of the centre if the diameter of the circle is 20 units.

Answer 1

Given diameter of the circle = 20 units.

∴ radius= 10units

OP=10 

`sqrt (("x" + 1 - 8)^2 + ("x" - 4 -5)^2)  = 10`

squaring both sides, 

x² + 49- 14x + x² = 81- 18x = 100 

⇒ 2x² - 32x + 30=0 

⇒ x² - 16x + 15=0 

⇒ x²  -15x - x +15 = 0 

⇒ (x - 15) (x - 1) = 0 

⇒ x = 15 or 1 

Coordinates of 0when x=15 are (16, 11) 

Coordinates of 0 when x = 1 are ( 2, - 3)