The equation of circle at center $(3, 4)$ and radius $5$ .

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

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x^{2} + y^{2} + 3 x + 4 y + 5 = 0

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

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Solution

The correct option is C $x^{2} + y^{2} - 6 x - 8 y = 0$
The center of equation $(3, 4)$
The radius of circle is $5$
The equation of circle is
$(x - 3)^{2} + (y - 4)^{2} = 5^{2} x^{2} + y^{2} - 6 x + 9 - 8 y + 16 = 25 x^{2} + y^{2} - 6 x - 8 y = 0$

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

k =

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

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