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Question

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

A
tan1(425)
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B
tan1(227)
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C
tan1(427)
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D
None of these
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Solution

The correct option is B tan1(427)
Let
y1=4x2 and y2=x2
Thus
4x2=x2
2x2=4
x2=2
x=±2

y=2
Hence the curves intersect at
(2,2) and (2,2)
Now slope of the curves at (2,2) is
y1|x=2=2x|2
=22
y2|2=2x|2
=22

Hence
tanθ=|y2y11+y1y2|

=|4218|

tanθ=427
θ=tan1(427)

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