Question

The locus of the middle points of chords of hyperbola $3x^2-2y^2+4x-6y=0$ parallel to $y=2x$ is :

• A. $3x-4y=4$
• B. $3x+4y=8$
• C. $5x-4y=9$
• D. $6x-3y=4$

Answer 1

The correct option is A $3x-4y=4$

By $T=S_1$ the equation of chord whose midpoint is $(h,k)$ is
$3xh-2yk+2(x+h)-3(y+k)=3h^2-2k^2+4h-6k$
$\Rightarrow x(3h+2)-y(2k+3)-2h+3k-3h^2+2k^2=0$
Its slope is $\frac{3h+2}{2k+3}=2$
$\because$ Its parallel to line $y=2x$
$\Rightarrow 3h-4k=4$
$\therefore 3x-4y=4$