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Question

If x = a cos t, y = a sin t, then d2ydx2 at t=π4 is

A
a22
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B
a22
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C
22a
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D
22a
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Solution

The correct option is D 22a
Clearly x2+y2=a2 and y(π4)=a2,x(π4)=a2. Differentiating we get,
2x+2yy1=0y1=xy,soy1(π4)=1
Now x+yy1=01+y21+yy2=0
y2(π4)=1+(y1(π4))2y(π4)=22a

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