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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.
Solution
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)
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