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Question

If sin1 a is the acute angle between the curves x2+y2=4x and x2+y2=8 at (2, 2), then a= _____

A
1
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B
0
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C
12
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D
32
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Solution

The correct option is B 12
Angle between the curves is given by the angle between their tangents at the given point.
For the curve x2+y24x=0,2x+2ydydx4=0
4dydx=44=0
dydx=0 at (2,2)
For the curve x2+y2=8,2x+2ydydx=0
dydx=xy=1 at (2,2)
tana=0(1)10(1)=1
sina=11+1=12
a=sin112

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