Question

The value of $c$, for which the line $y=2 x+c$ is a tangent to the circle $x^2+y^2=16$ is

(a) $-16 \sqrt{5}$

(b) $4 \sqrt{5}$.

(c) $16 \sqrt{5}$

(d) 20

Answer 1

SOLUTION — We know that, if $y=m x+c$ is tangent to the circle $x^2+y^2=a^2$, then $c= \pm a \sqrt{1+m^2}$, here $m=2, a=4$.

$$\therefore \quad c= \pm 4 \sqrt{1+2^2}= \pm 4 \sqrt{5}$$

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