Question

If the straight line $ y=2x+c $ is a tangent to the ellipse $ \frac{{{x}^{2}}}{3}+\frac{{{y}^{2}}}{4}=1, $ then c equals to

• A. $ \pm \,\,4 $
• B. $ \pm \,\,6 $
• C. $ \pm \,\,8 $
• D. $ \pm \,\,1 $

Answer 1

Answer: (A)

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 $