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Q.
An infinite number of tangents can be drawn from $\left(1, 2\right)$ to the circle $x^{2} + y^{2} -2x - 4y + \lambda = 0$ then $\lambda=$
Conic Sections
Solution:
Clearly the point $\left(1, 2\right)$ is the centre of the given circle and infinite tangents can only be drawn on a point circle. Hence the radius should be $0$.
$\therefore \sqrt{1^{2} +2^{2} -\lambda} =0 \Rightarrow \lambda =5$