Question

The values that m can take so that the straight line $y=4x+m$ touches the curve $x^2+4y^2=4$ is

• A. $\pm \sqrt{45}$
• B. $\pm \sqrt{60}$
• C. $\pm \sqrt{65}$
• D. $\pm \sqrt{72}$

Answer 1

Answer: (C)

$\pm \sqrt{65}$

The equation of tangent for an ellipse is $y=kx\pm \sqrt{a^2{k}^2+b^2}$
$m=\pm \sqrt{a^2{k}^2+b^2}$
here, $a=2,$ $b=1$ and $k=4$
$=\pm \sqrt{4\left(16\right)+1}=\pm \sqrt{65}$