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Question

Let θ be the acute angle between the curves y=|x22| and y=8x2 at their point(s) of intersection. Then the value of tanθ is

A
0
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B
35
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C
53
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D
1
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Solution

The correct option is C 53
y=|x22| and y=8x2
Points of intersection:
|x22|=8x2
x44x2+4=8x2x43x24=0(x2+1)(x24)=0x2=4x=±2
y=2

At x=2,
y=x22dydx=2xm1=dydx(2,2)=4y=8x2dydx=xym2=dydx(2,2)=1tanθ=4(1)14=53

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