Question

The line $4y-3x+\lambda =0$ touches the circle $x^2+y^2-4x-8y-5=0$. The value of $\lambda$ is

• A. $29$
• B. $10$
• C. $-35$
• D. None of these

Answer 1

Answer: (C)

$-35$

Since, line $4y-3x+\lambda =0$ touches the circle $x^2+y^2-4x-8y-5=0$

Then, radius = perpendicular distance

$\sqrt{2^2+4^2+5}=\left|\frac{-6+16+\lambda }{5}\right|$

$\Rightarrow \lambda =-35$
Ans: C