Question

The line $l x+m y+n=0$ will be a tangent to the carcle $x^2+y^2=a^2$, if

(a) $n^2\left(l^2+m^2\right)=a^2$

(b) $a^2\left(l^2+m^2\right)=n^2$

(c) $n(l+m)=a$

(d) $a(l+m)=n$

Answer 1

We know, line $y=m x+c$ is tangent, if $c= \pm a \sqrt{1+m^2}$

Given, $\quad y=-\frac{l}{m} x-\frac{n}{m}$

$\therefore \quad-\frac{n}{m}= \pm a \sqrt{1+\left(\frac{l}{m}\right)^2} \Rightarrow n^2=a^2\left(m^2+l^2\right)$

So, The correct option of this question will be (B).