Line $3 x + 4 y = 25$ touches the circle $x^{2} + y^{2} = 25$ at the point-

(4, 3)

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(3, 4)

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(- 3, - 4)

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none of these

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Solution

The correct option is A $(3, 4)$
Equation of tangent at $(x_{1}, y_{1})$ to the circle $x^{2} + y^{2} = 25$ is given by,
$x x_{1} + y y_{1} = 25$ . Now comparing it with $3 x + 4 y = 25$
We get required point of contact $(3, 4)$

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$x^{2} - y^{2} - 2 x + 4 y - 3 = 0,$ is

(1, - 5)

3 x + 4 y = 8,

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