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

3 x - 4 y = 4

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

3 x - 4 y + 4 = 0

No worries! We‘ve got your back. Try BYJU‘S free classes today!

4 x - 4 y = 3

No worries! We‘ve got your back. Try BYJU‘S free classes today!

3 x - 4 y = 2

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A $3 x - 4 y = 4$
Let the mid point be $(h, k)$ .

Equation of a chord whose mid point is $(h, k)$ would be $T = S_{1}$

$\Rightarrow 3 x h - 2 y k + 2 (x + h) - 3 (y + k) = 3 h^{2} - 2 k^{2} + 4 h - 6 k \Rightarrow x (3 h + 2) - y (2 k + 3) - (2 h + 3 k) - 3 h^{2} + 2 k^{2} = 0$

Its slope is $\frac{3 h + 2}{2 k + 3} = 2$ (given) $\Rightarrow 3 h = 4 k + 4$

$∴$ Required locus is $3 x - 4 y = 4$ .

Suggest Corrections

Similar questions

3 x^{2} - 2 y^{2} + 4 x - 6 y = 0

3 x^{2} - 2 y^{2} + 4 x - 6 y = 0

y = 2 x

3 x^{2} - 2 y^{2} + 4 x - 6 y = 0

y = 2 x

3 x^{2} - 2 y^{2} + 4 x - 6 y = 0

y = 2 x

3 x^{2} - 2 y^{2} + 4 x - 6 y = 0

y = 2 x

Join BYJU'S Learning Program