If \(y=\sqrt{3} x+k_1\) and \(y=\sqrt{3} x+k_2\) are two parallel tangents of a circle of radius 2 units,…
If \(y=\sqrt{3} x+k_1\) and \(y=\sqrt{3} x+k_2\) are two parallel tangents of a circle of radius 2 units, then \(\left|k_1-k_2\right|\) is equal to
1
8
4
2
Solution
The distance between parallel tangents to a circle is equals to the diameter of the circle, so
\(\begin{aligned}
& \frac{\left|k_1-k_2\right|}{\sqrt{1+3}}=4 \\
\Rightarrow \quad & \left|k_1-k_2\right|=8
\end{aligned}\)
Hence, option (b) is correct.
