Q. The angle between the line joining origin and intersection points of line $2x + y = 1$ and curve $3x^{2} + 4yx - 4x + 1 = 0$ is
A) $\pi/2$
B) $\pi/3$
C) $\pi/4$
D) $\pi/6$
Explanation
(a)
The equation of required line is
${3x}^{2} + 4xy - 4x(2x + y) + {(2x + y)}^{2} = 0$
$\Rightarrow \ {3x}^{2} + 4xy - 8x^{2} - 4xy + 4x^{2} + y^{2} + 4xy = 0$
$\Rightarrow \ - x^{2} + y^{2} + 4xy = 0$
(Coefficient of $x^{2}) +$(Coefficient of $y^{2}) = - 1 + 1 = 0$
$\therefore$ Lines are mutually perpendicular.
$ie,\ Angle\ between\ lines\ is\frac{\pi}{2}.$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.