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

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Ans: (A) & (B)

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.