Question

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

• A. $\lambda =20$
• B. $\lambda =-20$
• C. $\lambda =5$
• D. no such $\lambda$ exists

Answer 1

The correct option is C $\lambda =5$

$x^2+y^2-2x-4y+\lambda =0$
Centre is $(1,2)$
Infinite tangents from $(1,2)$ are possible only if it is a point circle.
$\therefore r=0$
$\Rightarrow \lambda =5$