Question

For what value of $\lambda$, the line $4x+3y+\lambda =0$ will be tangent to the circle $x^2+y^2-6x+4y-12=0$ ?

• A. $19$
• B. $-19$
• C. $-31$
• D. $31$

Answer 1

Answer: (A), (C)

The correct options are
A $19$
C $-31$

Centre and the radius of the circle are $(3,-2)$ and $\sqrt{9+4+12}=5$
Thus for given line to be tangent to the circle, the distance of line from centre of the
circle should be equal to it's radius.
$\Rightarrow \left|\frac{4\left(3\right)+3(-2)+\lambda }{\sqrt{3^2+4^2}}\right|=5$
$\Rightarrow 6+\lambda =\pm 25\Rightarrow \lambda =19,-31$