The chords lx + my = 1 (l, m being parameters) of the curve $x^{2} - 3 y^{2} + 3 x y + 3 x = 0$ that subtend a right angle at origin, are concurrent at the point

(\frac{3}{2}, 0)

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

(\frac{1}{2}, 0)

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

(- \frac{3}{2}, 0)

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

(1, 0)

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

Open in App

Solution

The correct option is A $(\frac{3}{2}, 0)$
The pair of lines $x^{2} - 3 y^{2}$ + 3xy + 3x(lx + my) = 0 are perpendicular to each other
$\Rightarrow 1 - 3 + 3 l = 0 \Rightarrow l = \frac{2}{3}$
$\Rightarrow$ Chords are 2x – 3 + my = 0 which always pass through $(\frac{3}{2}, 0)$

Suggest Corrections

Similar questions

2 x^{2} + 3 y^{2} - 5 x = 0

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

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

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

x^{2} + y^{2} + 2 g x + 2 f y + c = 0

\frac{l g + m f + 1}{l^{2} + m^{2}} =

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

(a, b)

| a | + | b |

Join BYJU'S Learning Program