Q: The angle between the hyperbola xy = c^{2} and x^{2} – y^{2} = a^{2} is

(A) independent of c

(B) dependent on a

(C) always p/3

(D) none of these

Sol. Differentiating xy = c^{2} with respect to x, we get

$\large \frac{dy}{dx} = -\frac{y}{x}$

Differentiating x^{2} – y^{2} = a^{2} with respect to x, we get

$\large \frac{dy}{dx} = \frac{x}{y}$

Clearly the two curves always intersect orthogonally.

Hence (A) and (B) are the correct answers.