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Question
Find the centre and radius of the following:
4x2 + 4y2 − 24x − 8y − 24 = 0
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Solution
The given equation, after dividing it by 4, can be written as:
x2 + y2 − 6x − 2y − 6 = 0
Comparing it with the equation
x2 + y2 + 2gx + 2fy + c = 0, we get,
2g = − 6, 2f = − 2 and c = − 6
∴ g = − 3, f = − 1 and c = − 6
∴ centre of the circle = ( − g, − f) = (3, 1)
and radius of the circle = `sqrt("g"^2 + "f"^2 - "c")`
= `sqrt((-3)^2 + (-1)^2 - (-6))`
= `sqrt(9 + 1 + 6)`
= 4.
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