Q. The locus of middle points of chords of hyperbola $3x^{2} - 2y^{2} + 4x - 6y = 0$ parallel to $y = 2x$ is
A) $3x - 4y = 4$
B) $3y - 4x + 4 = 0$
C) $4x - 3y = 3$
D) $3x - 4y = 2$
Explanation
(a)
Let $(h,k)$ is mid point of chord.
Then, its equation is $T = S_{1}$
$\therefore 3hx - 2ky + 2(x + h) - 3(y + k) = 3h^{2} - 2k^{2} + 4h - 6k$
$x(3h + 2) + y( - 2k - 3) = 3h^{2} - 2k^{2} + 2h - 3k$
Since, this line is parallel to $y = 2x$
$\frac{3h + 2}{2k + 3\ } = 2$
$\Rightarrow \ 3h - 4k = 4$
Thus, locus of point is $3x - 4y = 4$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.