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Find the centre and radius of the following: x2 + y2 − 6x − 8y − 24 = 0 - Mathematics and Statistics

Sum

Find the centre and radius of the following:

x2 + y2 − 6x − 8y − 24 = 0

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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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