Question

The angle between the pair of straight lines formed by joining the points of intersection of $x^2+y^2=4$ and $y=3x+c$ 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, $x^2+y^2=4{\left(\frac{y-3x}{c}\right)}^2$
$\Rightarrow c^2\left(x^2+y^2\right)=4\left(y^2+9x^2-6xy\right)$
These lines are perpendicular.
$\therefore$ coefficient of $x^2+$ coefficient of $y^2=0$
$\Rightarrow c^2-36+c^2-4=0$
$\Rightarrow 2c^2=40$
$\Rightarrow c^2=20$