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Question
Find the centre and radius of the following:
x2 + y2 − 6x − 8y − 24 = 0
Solution
Given equation of the circle is
x2 + y2 − 6x − 8y − 24 = 0
Comparing this equation with
x2 + y2 + 2gx + 2fy + c = 0, we get
2g = − 6, 2f = − 8 and c = − 24
∴ g = − 3, f = − 4 and c = − 24
∴ Centre of the circle = (−g, −f) = (3, 4)
and radius of the circle = `sqrt("g"^2 + "f"^2 - "c")`
= `sqrt((- 3)^2 + (- 4)^2 - (- 24))`
= `sqrt(9 + 16 + 24)`
= `sqrt(49)`
= 7.
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