1. Tardigrade
  2. Question
  3. Mathematics
  4. The number of values of c such that the straight line y = 4x + c touches the curve (x2/ 4) + y2 = 1 is

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. 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

IIT JEEIIT JEE 1998Conic Sections

Solution:

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 $
$\Rightarrow c= \pm \sqrt{65}$