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Question
Find the centre and radius of the circle.
5x2 + 5y2+ 4x – 8y – 16 = 0
Solution
To make coefficient of x2 unity, divide the equation by 5 we get,
`x^2 + y^2 + 4/5 x - 8/5 y - 16/5 = 0`
Comparing the above equation with x2 + y2 + 2gx + 2fy + c = 0 we get,
2g = `4/5`, 2f = `-8/5`, c = `(- 16)/5`
∴ g = `2/5`, f = `- 4/5`, c = `(-16)/5`
Centre = (-g, -f) = `((-2)/5, 4/5)`
Radius = `sqrt("g"^2 + "f"^2 - "c"^2)`
`= sqrt((2/5)^2 + ((-4)/5)^2 - ((-16)/5))`
`= sqrt(4/25 + 16/25 + 16/5)`
`= sqrt((4 + 16 + 16 xx 5)/25)`
`= sqrt((20 + 80)/25)`
`= sqrt(100/25)`
`= sqrt4` = 2
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