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Question

If (x2+y2)=a.etan1(y/x) a>0,then y"(0) is equal to

A
2aeπ/2
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B

aeπ/2
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C
2aeπ/2
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D
Does not exist
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Solution

The correct option is C 2aeπ/2
(x2+y2)=a.etan1(y/x)
12x2+y2(2x+2yy) =a.etan1(y/x)×11+y2x2×xyyx2.....(i)
x+yyx2+y2=(x2+y2)×xyyx2+y2
[from Eq.(i)]
x+yy=xyyy=x+yxy
y"=2(xyy)(xy)2
y"(0)=2(0y(0)){0y(0)}2=2aeπ/2=2aeπ/2

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