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Question

If the curves y = 2 ex and y = ae−x intersect orthogonally, then a =

(a) 1/2
(b) −1/2
(c) 2
(d) 2e2

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Solution

(a) 1/2

Given:y=2ex ...1y=ae-x ...2Let the point of intersection of these curves be x1, y1.On differentiating (1) w.r.t. x, we getdydx=2exm1=dydx x1, y1=2ex1Now, on differentiating (2) w.r.t. x, we getdydx=-ae-xm2=dydx x1, y1=-ae-x1It is given that the curves are orthogonal.m1×m2=-12ex1×-ae-x1=-12a=1a=12

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