The center of the circle given by the equation $x^{2} + y^{2} - 4 x + 6 y - 51 = 0$ is .

(2,-3)

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(-2,3)

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(3,-2)

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(-3,2)

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Solution

The correct option is A (2,-3)
On comparing the given equation with the standard equation of circle i.e. $x^{2} + y^{2} + 2 g x + 2 f y + c = 0$ , We get:
2g=-4 and 2f=6
$⟹$ g=-2 and f=3
Also the center of the circle is (-g,-f)
$⟹$ the center of the given circle will be (2,-3)

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2^{nd}

4^{th}

What is the equation of the chord centered at (1, 2) in the circle $x^{2} + y^{2} - 4 x - 6 y - 10 = 0$

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