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, $c=\sqrt{a^2{m}^2+b^2}$
$\Rightarrow$ $c=\sqrt{(3){(2)}^2+(4)}$ $\left(\because \{\begin{array}{c}m=2\\ a^2=3\\ b^2=4\end{array}\right)$
$\Rightarrow$ $c=\sqrt{12+4}=\sqrt{16}$
$c=\pm 4$