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Question

The distance, from the origin, of the normal to the curve,x=2cost+2tsint,y=2sint2tcost, at t=π4,is:

A
4
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B
2
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C
2
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D
22
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Solution

The correct option is C 2
x=2cost+2tsint,dxdt=2tcosty=2sint2tcostdydt=2tsintdydx=tant
So, slope of normal at t=π4 is 1tant=1
Equation of normal at
t=π4x+y22=0
Distance of normal form the Origin= 221+1=2 units

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