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Obtaining Centre and Radius of a Circle from General Equation of a Circle

The radius of...

Question

The radius of circle $x^{2} + y^{2} - 12 x + 8 y + 32 = 0,$ is

A

2 \sqrt{5}

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B

\sqrt{10}

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C

4 \sqrt{11}

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D

\sqrt{5}

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Solution

The correct option is A $2 \sqrt{5}$
Equation of circle is :
$x^{2} + y^{2} - 12 x + 8 y + 32 = 0$
Comparing with general equation of circle :
$x^{2} + y^{2} + 2 g x + 2 f y + c = 0$
Centre $(- g, - f) = (6, - 4)$
And radius is,
$r = \sqrt{g^{2} + f^{2} - c} = \sqrt{36 + 16 - 32} = \sqrt{20} = 2 \sqrt{5}$

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