A) \[\pm \,\,4\]
B) \[\pm \,\,6\]
C) \[\pm \,\,8\]
D) \[\pm \,\,1\]
Correct Answer: A
Solution :
Given that, the straight line \[y=2x+c\] is the tangent to the ellipse \[\frac{{{x}^{2}}}{3}+\frac{{{y}^{2}}}{4}=1.\] Then by condition, \[c=\sqrt{{{a}^{2}}{{m}^{2}}+{{b}^{2}}}\] \[\Rightarrow \] \[c=\sqrt{(3){{(2)}^{2}}+(4)}\] \[\left( \because \,\,\,\left\{ \begin{matrix} m=2 \\ {{a}^{2}}=3 \\ {{b}^{2}}=4 \\ \end{matrix} \right. \right)\] \[\Rightarrow \] \[c=\sqrt{12+4}=\sqrt{16}\] \[c=\pm 4\]
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