If foci of hyperbola lie on y = x and one of the asymptotes is y = 2x, then equation of the hyperbola, given that it passes through (3, 4), is

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

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

None of these

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

Open in App

Solution

The correct option is C
Foci of hyperbola lie on y = x. So, the major axis is y = x. Major axis of hyperbola bisects the asymptote.
$\Rightarrow$ Equation of hyperbola is x = 2y
$\Rightarrow$ Equation of hyperbola is (y – 2x)(x – 2y) + k = 0
Given that, it passes through (3, 4)
$\Rightarrow$ Hence, required equation is
$2 x^{2} + 2 y^{2} - 5 x y + 10 = 0$

Suggest Corrections

Similar questions

2 x^{2} + 5 x y + 2 y^{2} - 11 x - 7 y - 4 = 0

The equations of the asymptotes of the hyperbola $2 x^{2} + 5 x y + 2 y^{2} - 11 x - 7 y - 4 = 0$ are

y = x

y = 2 x

(3, 4)

x + y = 2

P (1, 1)

A

B

A B = 6 \sqrt{2}

A pair of tangents are drawn from the origin to the circle $x^{2} + y^{2} + 20 (x + y) + 20 = 0$ . The equation of the pair of tangents is

Join BYJU'S Learning Program