Question

The number of values of $c$ such that the straight line $y=4x+c$ touches the curve $\frac{x^2}{4}+y^2=1$ is

• A. 0
• B. 2
• C. 1
• D. $\infty$

Answer 1

Answer: (B)

For ellipse, condition of tangency is $c^2=a^2{m}^2+b^2$
Given line is $y=4x+c$ and curve $\frac{x^2}{4}+y^2=1$
$\Rightarrow c^2=4\times 4^2+1=65$
$\Rightarrow c=\pm \sqrt{65}$