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

Answer 1

The correct option is C $5$

We have,

Equation of circle is

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

Given points $(1,2)$, 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.