Q. The number of values of $c$ such that the line $y = 4x + c$ touches the curve $\frac{x^{2}}{4} + y^{2} = 1\$ is
A) 1
B) 2
C) $\infty$
D) 0
Explanation
(b)
Given, $y = 4x + c$ 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
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.