Question

The angle between the pair of straight lines formed by joining the points of intersection of $x^{2}+y^{2}=4$ and $y=3 x +c$ to the origin is a right angle. Then $c^{2}$ is equal to

• A. 20
• B. 13
• C. 1 / 5
• D. 5

Answer 1

Answer: (A)

Since, the angle is right angle.
$\therefore $ Homogenising, $x^{2}+y^{2}=4\left(\frac{y-3 x}{c}\right)^{2}$
$\Rightarrow c^{2}\left(x^{2}+ y^{2}\right)=4\left(y^{2}+9 x^{2}-6 x y\right)$
These lines are perpendicular.
$\therefore $ coefficient of $x^{2}+$ coefficient of $y^{2}=0$
$\Rightarrow c^{2}-36+c^{2}-4=0$
$\Rightarrow 2 c^{2}=40$
$\Rightarrow c^{2}=20$