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Question
Find the centre and radius of the circle.
(x + 2) (x – 5) + (y – 2) (y – 1) = 0
Solution
Equation of the circle is (x + 2) (x – 5) + (y – 2) (y – 1) = 0
x2 – 3x – 10 + y2 – 3y + 2 = 0
x2 + y2 – 3x – 3y – 8 = 0
Comparing this with x2 + y2 + 2gx + 2fy + c = 0
We get 2g = -3, 2f = -3, c = -8
g = `(-3)/2,` f = `(-3)/2`, c = - 8
Centre (-g, -f) = `(3/2, 3/2)`
Radius = `sqrt("g"^2 + "f"^2 - "c"^2)`
= `sqrt(9/4 + 9/4 + 8)`
`= sqrt(18/4 + 8)`
`= sqrt(9/2 + 8)`
`= sqrt((9+16)/2)`
`= sqrt(25/2)`
`= 5/sqrt2`
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