Q. 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) 30
C) 1/5
D) 5
Explanation
(a)
Since, the angle is right angle.
$\therefore Homogenising,\ x^{2} + y^{2} = 4\left( \frac{y - 3x}{c} \right)^{2}$
$\Rightarrow \ c^{2}\left( x^{2} + y^{2} \right) = 4\left( y^{2} + 9x^{2} - 6xy \right)$
Since, lines are at right angle.
$\therefore\ Coefficient\ of\ x^{2} + coefficient\ of\ y^{2} = 0$
$\Rightarrow \ c^{2} - 36 + c^{2} - 4 = 0$
$\Rightarrow \ c^{2} = 20$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.