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