If the line $y=2 x+c$ is a tangent to the circle $x^2+y^2=5$, then a value of $c$ is

• A

  2
• B

  3
• C

  4
• Correct answer
  D

  5

Solution

Here, $\quad m=2$ and $c_1=c$ Given equation of circle is $x^2+y^2=5$ Here radius $a=\sqrt{5}$ Since, the line (i) is tangent to the circle. $\begin{aligned} & \therefore \quad c=a \sqrt{m^2+1}=\sqrt{5} \sqrt{(2)^2+1} \\ & \Rightarrow \quad c=\sqrt{5} \cdot \sqrt{5}=5 \\ & \end{aligned}$

Hence, the correct answer is option: 'D'.