Q97 / 160 · TS EAMCET 2023 (14 May Shift 2) · Mathematics

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

  • A
    $\pm 13$
  • B
    $\pm 7$
  • Correct answer
    C
    $\pm \sqrt{65}$
  • D
    $\pm \sqrt{74}$

Solution

$y=4 x+c$ $\Rightarrow \quad \frac{x^2}{4}+\frac{y^2}{1}=1$ If $y=m x+c$ is tangent then $\begin{aligned} & c^2=a^2 m^2+b^2 \\ & \Rightarrow \quad c^2=4(4)^2+1^2=65 \\ & \therefore \quad c^2= \pm \sqrt{65} .\end{aligned}$

Hence, the correct answer is option: 'C'.

Relevant Questions