The number of tangents to the circle $x^{2} + y^{2} - 8 x - 6 y + 9 = 0$ which passes through the point $(3, - 2)$ is

2

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1

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0

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None of these

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Solution

The correct option is D $2$
Let $S \equiv x^{2} + y^{2} - 8 x - 6 y + 9 = 0$
Now $s$ for $(- 3, 2) = 9 + 4 - 24 + 12 + 9 > 0$
$∴$ the point $(3, - 2)$ lies outside the circle.
$∴$ $2$ tangents can be drawn to the circle from the point $(3, - 2)$

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