Question

The value of $c$, for which the line $ y = 2x + 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

Answer: (B)

Given that, $y = 2x + c \quad ...(i)$
and $x^2 + y^2 = 16\quad ...(ii)$
We know that $y = mx + c$ 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 c = \pm 4 \sqrt{1+2^2} $
$= \pm 4 \sqrt 5$