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Question

Find the condition that curves 2x=y2 and 2xy = k inersect orthogonally.
 


Solution

Given equation of curves are 2x=y2and 2xy=k y=k2xfrom eq(i), 2x=(k2x)28x3=k2x3=18k2x=12k23y=k2x=k212k23=k13
From Eqs. (i) and (ii), 
2=2ydydx
and 2[x.dydx+y.1]=0dydx=1yand(dydx)=2y2x=yx(dYdx)(12k23k13)=k1312K23=2K13
Since, the curves intersect orthogonally.
i.e., m1.m2=11k13.(2k13)=12k23=12k23=1k23=2k2=8
 

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