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
B
0
C
5
D
can no be determined

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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