Find the equation of tangent drawn at the point $(3, - 4)$ on the circle $x^{2} + y^{2} = 25$ .

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Solution

Let the circle is -point $(3, - 4)$
$x^{2} + y^{2} + 2 g x + 2 f y + c = 0$
$x^{2} + y^{2} = 25$

Therefore,
$a + 16 + 6 g - 8 f + c = 0$
$c - 25 = 0 \Rightarrow c = 25$
$25 + 6 g - 8 f + 25 = 0$
$6 g - 8 f + 50 = 0$

The circle of the centre $(- g, - f)$
$- 6 x + 8 y + 50 = 0$
$6 x - 8 y - 50 = 0$

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