Question

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. $3x-4y=2$

Answer 1

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

Given hyperbola is, $3x^2-2y^2+4x-6y=0$
Let $P(h,k)$ be the mid point of chord,
Thus equation of chord with 'P' as middle point is $T=S_1$
$3hx-2ky+2(x+h)-3(y+k)=3h^2-2k^2+4h-6k$
$\Rightarrow (3h+2)x-(2k+3)y+2k^2-3h^2-2h+3k=0$
But given this line is parallel to $y=2x$
$\Rightarrow \frac{3h+2}{2k+3}=2$
$\Rightarrow 3h-4k=4$
Hence locus of $P(h,k)$ is, $3x-4y=4$