Question

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

(A) x² - y² - 5/2 xy + 5= 0

(B) 2x² - 2y² + 5xy + 10 = 0

(C) 2x² + 2y² - 5xy + 10 = 0

(D) None of these

Answer 1

Correct option is (C) 2x² + 2y² - 5xy + 10 = 0

Foci of hyperbola lie on y = x.

So, the equation of transverse axis is y − x = 0.

Transverse axis of hyperbola bisects the asymptote

⇒ equation of other asymptote is y = \(\frac x2\)

or, x = 2y

⇒ Equation of hyperbola is (y − 2x)(x − 2y) + k = 0

Since, it passes through (3, 4)

⇒ k = −10

Hence, required equation is 2x² + 2y² − 5xy + 10 = 0.