Question

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

• A. $x^2-y^2-\frac{5}{2}xy+5=0$
• B. $2x^2-2y^2+5xy+5=0$
• C. $2x^2+2y^2-5xy+10=0$
• D. None of these

Answer 1

The correct option is C $2x^2+2y^2-5xy+10=0$

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
$2x^2+2y^2-5xy+10=0$