Find the equation of the circle :
Centered at $(3, - 2)$ with radius $4$ .

x^{2} + y^{2} + 6 x - 4 y = 3

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x^{2} + y^{2} - 6 x + 4 y = 3

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x^{2} + y^{2} - 3 x + 2 y = - 3

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x^{2} + y^{2} + 3 x - 2 y = - 3

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Solution

The correct option is B $x^{2} + y^{2} - 6 x + 4 y = 3$
The center radius form equation of circle is $(x - h)^{2} + (y - k)^{2} = r^{2}$ , where $(h, k)$ is the center and $r$ is the radius.
Here, $(h, k) \equiv (3, - 2)$ and $r = 4$
$∴$ Equation of circle: - $(x - 3)^{2} + (y - (- 2))^{2} = 4^{2} \Rightarrow x^{2} + 9 - 6 x + y^{2} + 4 + 4 y = 16 \Rightarrow x^{2} + y^{2} - 6 x + 4 y = 3$

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