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Question

The curves y = aex and y = bex cut orthogonally, if

(a) a = b
(b) a = −b
(c) ab = 1
(d) ab = 2


Solution

(c) ab = 1

Given:y=aex     ...1y=be-x   ...2Let the point of intersection of these two curves be x1, y1.Now,On differentiating (1) w.r.t. x, we getdydx=aexm1=dydx x1, y1 =aex1Again, on differentiating (2) w.r.t. x, we getdydx=-be-xm2=dydx x1, y1=-be-x1It is given that the curves cut orthogonally.m1×m2=-1aex1×-be-x1=-1ab=1

Mathematics
RD Sharma XII Vol 1 (2015)
Standard XII

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