Q. The equation of the pair of straight lines perpendicular of the pair ${2x}^{2} + 3xy + 2y^{2} + 10x + 5y = 0$ and passing through the origin, is
A) ${2x}^{2} + 5xy + 2y^{2} = 0$
B) $2x^{2} - 3xy + {2y}^{2} = 0$
C) ${2x}^{2} + 3xy + y^{2} = 0$
D) ${2x}^{2} - 5xy + {2y}^{2} = 0$
Explanation
(b)
We know that equation of pair of straight line passing through the origin and perpendicular to ${ax}^{2} + 2hxy + {by}^{2} = 0$ is
${bx}^{2} - 2hxy + {ay}^{2} = 0$
$\therefore$ Required equation of pair of straight line is
${2x}^{2} - 3xy + {2y}^{2} = 0$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.