Question

The locus of middle point 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. $3x-4y=2$

Answer 1

Answer: (A)

Let $(h,k)$ be mid-point of chord.

Then, its equation is $T=S_1$

$\therefore 3hx-2ky+2\left(x+h\right)-3\left(y+k\right)$

$=3h^2-2k^2+4h-6k$

$\Rightarrow x\left(3h+2\right)+y\left(-2k-3\right)$

$=3h^2-2k^2+2h-3k$

Since, this line is parallel to $y=2x$

$\therefore \frac{3h+2}{2k+3}=2$

$\Rightarrow 3h+2=4k+6$

$\Rightarrow 3h-4k=4$

Thus, locus of point is
$3k-4y=4$