Question

The number of values of $C$ for which the line $y=4x+c$ touch the curve $\frac{x^2}{4}+y^2=1$.

• A. $0$
• B. $1$
• C. $2$
• D. $\infty$

Answer 1

Answer: (C)

$2$

The given curve $\frac{x^2}{4}+y^2=1$ is an ellipse

Here, $a=2$ and $b=1$

And equation of line is slope form is $y=mx+c$

Also, $c=\sqrt{a^2{m}^2+b^2}$
$\Rightarrow c=\sqrt{4\left(16\right)+1}=\pm \sqrt{65}$
Hence, $c$ has two values.