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Question

Find the angle of intersection of the curves y=4x2and y=x2

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Solution

We have y=4x2
and y=x2dydx=2xand dydx=2xm1=2xand m2=2xfrom Eqs.(i) and (ii)x2=4x22x2=4x2=2x=±2y=x2=(±2)2=2
So, the points of intersection are (2,2) and (2,2).
For point (+2,2),m1=2x=2.2=22
and m2=2x=22.
For point (2,2),tanθ=m1m21+m1m2=2222122.22=427θ=tan1(427)


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