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Question

If the acute angles between the curves y=|x21| and y=|x23| at their points of intersection be θ such that tanθ=m7 then m2 is equal to :

A
6
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B
8
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C
10
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D
32
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Solution

The correct option is D 32
We have,
y=x21y=x23Pointofintersectionofcurvesx2=2x=±2Now,y=x21dydx=2xdydxx=2=22and,y=3x2dydx=2xdydxx=2=22Now,tanθ=m1m21+m1ml2=22+2218tanθ=427m=42m2=16×2=32Hence,theoptionDisthecorrectanswer.

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