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Question

The normal to the curve x=a(1cosθ), y=asinθ at θ always passes through the fixed point

A
(0,0)
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B
(0,a)
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C
(a,0)
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D
(a,a)
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Solution

The correct option is C (a,0)

dx=asinθ.dθ
dy=acosθ.dθ
Or
dxdy=tanθ.
Thus
Equation of normal will be
yasinθ=tanθ(xa+acosθ)
Or
cosθ.yasinθ.cosθ=xsinθ+asinθasinθcosθ
cosθ.y+sinθ.x=asinθ
Hence it passes through the fixed point (a,0).


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