An infinite number of tangents can be drawn from (1, 2) to circle {x^2} + {y^2} - 2x - 4y + λ = 0 ,

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10-1.Circle and System of Circles

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

A

$-20$

B

$0$

C

$5$

D

Cannot be determined

Solution

(c) Clearly the point $(1, 2)$ is the centre of the given circle and infinite tangents can only be drawn on a point circle.

Hence radius should be $0$.

$\therefore \,\sqrt {{1^2} + {2^2} – \lambda } = 0 $

$\Rightarrow \lambda = 5$.

Standard 11

Mathematics

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