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 y - 4 x + 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 $(G, K)$ be the mid-point of a chord of the hyperbola ${3 x}^{2} - {2 y}^{2} + 4 x - 6 y = 0$ . Then the equation of the chord is
$3 h x - 2 k y + 2 (x + h) - 3 (y + k) = {3 h}^{2} - {2 k}^{2} + 4 h - 6 k [u s i n g T = S^{'}]$
This is parallel to $y = 2 x$
$∴ \frac{- (3 h + 2)}{- (2 k + 3)} = 2 \Rightarrow 3 h + 2 = 4 k + 6$
$\Rightarrow 3 h - 4 k = 4$
Therefore, the locus of $(h, k)$ is $3 x - 4 y = 4$
Hence, option 'A' is correct.

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