question_answer

If the line \[x-2y=k\]cuts off a chord of length 2 from the circle \[{{x}^{2}}+{{y}^{2}}=3\], then k =

A)            0    

B)            \[\pm 1\]

C)            \[\pm \sqrt{10}\]                      

D)            None of these

Correct Answer: C

Solution :

           Obviously \[BC=\sqrt{2}\]                    Hence, \[\pm \frac{0-2.0-k}{\sqrt{{{1}^{2}}+{{(-2)}^{2}}}}=\sqrt{2}\Rightarrow k=\pm \sqrt{10}\].