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Question: The angle of intersection of the two curves xy = a<sup>2</sup> and x<sup>2</sup> + y<sup>2</sup> = ...

The angle of intersection of the two curves xy = a2 and

x2 + y2 = 2a2 is

A

π6\frac{\pi}{6}

B

π3\frac{\pi}{3}

C

π4\frac{\pi}{4}

D

None of these

Answer

None of these

Explanation

Solution

xy = a2 ⇒ y = a2x\frac{a^{2}}{x}⇒ dydx=−a2x2\frac{dy}{dx} = \frac{- a^{2}}{x^{2}} …(1)

Also x2 + y2 = 2a2 ⇒ dydx=−xy\frac{dy}{dx} = \frac{- x}{y} …(2)

point of intersection = (a, a)

∴ m1 = slope of (1) = –1

∴ m2 = slope of (2) = –1

Q m1 = m2 = – 1 ⇒ angle is 0 or π