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Question

an infinite number of tangents  can be drawn from (1,2) to the circle $$ x^2+ y^2-2x-4y+ \lambda=0$$ then $$lambda$$ is


A
20
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B
0
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C
5
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D
can no be determined
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Solution

The correct option is C $$5$$

We have,

Equation of circle is

$${{x}^{2}}+{{y}^{2}}-2x-4y+\lambda =0\,$$

Given points $$\left( 1,2 \right)$$, tangents are  drawn the circle

So,

$$ {{1}^{2}}+{{2}^{2}}-2\times \left( 1 \right)-4\times \left( 2 \right)+\lambda =0\, $$

$$ \Rightarrow 5-10+\lambda =0\, $$

$$ \Rightarrow \lambda =5 $$

Hence, this is the answer.


Mathematics

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