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Tangent

If the straig...

Question

If the straight line $y = m x + c$ touches the circle $x^{2} + y^{2} - 2 x - 4 y + 3 = 0$ at the point $(2, 3)$ , then $c =$

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5

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Solution

The correct option is C $5$
$\begin{matrix} x^{2} + y^{2} - 2 x - 4 y + 3 = 0 c e n t r e, (+ 1, + 2) r a d i u s = \sqrt{1^{2} + 2^{2} - 3} = \sqrt{2} l i n e t o u c h e s a t (2, 3) ∴ S l o p e o f n o r m a l = \frac{3 - 2}{2 - 1} = 1 ∴ S l o p e o f tan g e n t = - 1 y = - x + c l i n e p a s s e s t h r o u g h (2, 3) s o 2 + 3 = c o r c = 5 \end{matrix}$

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