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Question

The angle of intersection of the curves xy = a2 and x2 − y2 = 2a2 is

(a) 0°
(b) 45°
(c) 90°
(d) none of these

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Solution

(c) 90°

Given:xy=a2 ...1x2-y2=2a2 ...2Let x1, y1 be the point of intersection.On differentiating (1) w.r.t. x, we getxdydx+y=0dydx=-yxm1=dydxx1, y1=-y1x1On differentiating (2) w.r.t. x, we get2x -2y dydx=0dydx=xym2=dydxx1, y1=x1y1Now, m1×m2=-y1x1×x1y1 m1×m2=-1m1×m =-1So, the angle between the curves is 90°.

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