Question

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

• A. 0
• B. 1
• C. 2
• D. infinite

Answer 1

Answer: (C)

Given, $y=4 x+c$ and $\frac{x^{2}}{4}+y^{2}=1$
Condition for tangency,
$c^{2}=a^{2} m^{2}+b^{2}$
$\therefore \,\,\,\,\,\, c^{2}=4(4)^{2}+1^{2} $
$\Rightarrow \,\,\,\,\,\, c^{2} =65$
$\Rightarrow \,\,\,\,\,\, c=\pm \sqrt{65} $
Hence, for two values of $c$, the line touches the curve.