In the circle is concentric with the circle $x^{2} + y^{2} - 4 x - 6 y + 9 = 0$ and passes through the points $(4, 5)$ equation is

x^{2} + y^{2} + 4 x + 6 y - 5 = 0

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x^{2} + y^{2} - 4 x + 6 y + 5 = 0

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x^{2} + y^{2} - 4 x - 6 y + 5 = 0

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x^{2} + y^{2} + 4 x + 6 y + 5 = 0

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Solution

The correct option is C $x^{2} + y^{2} - 4 x - 6 y + 5 = 0$
The equation of circle is $x^{2} + y^{2} - 4 x - 6 y + 9 = 0$
The concentric circle is given as $x^{2} + y^{2} - 4 x - 6 y + k = 0$
It passes through is $(4, 5)$ is $4^{2} + 5^{2} - 4 (4) - 6 (5) + k = 0 16 + 25 - 16 - 30 + k = 0 k = 5$
The equation of circel is $x^{2} + y^{2} - 4 x - 6 y + 5 = 0$

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2^{nd}

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x^{2} + y^{2} + 4 x - 6 y + 9 {sin}^{2} α + 13 {cos}^{2} α = 0

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The diameters of a circle are along $2 x + y - 7 = 0$ and $x + 3 y - 11 = 0$ Then the equation of this circle, which also passes through (5,7) is

x^{2} + y^{2} - 8 x + 6 y - 5 = 0

(- 2, - 7)

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