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. 3y – 4x + 4 = 0
• C. 4x – 4y = 3
• D. 3x – 4y = 2

Answer 1

The correct option is A 3x – 4y = 4

By T = S1, the equation of chord whose mid-point is $(\alpha ,\beta )$ is $3x\alpha -2y\beta +(x+\alpha )-2(y+\beta )=0$
$\Rightarrow$ $x(3\alpha +2)-y(2\beta +3)=2$
as it is parallel to y = 2x
$\therefore$ $3\alpha –4\beta =4$
$\therefore$ Required locus is 3x – 4y = 4