The normal to the curve x=a(1+cos⁡θ), y=asin⁡θ at θ  always passes through the fixed point

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

  1. A

    (α, α)

  2. B

    (α, 0)

  3. C

    (0, α)

  4. D

    none of these

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    Solution:

    We have,

                 x=a(1+cosθ),y=asinθ. dydx=dθdx=acosθasinθ=cotθ

    The equation of the normal at (a(1+cosθ), asinθ) is 

         yasinθ=tanθ{xa(1+cosθ)}xsinθycosθ=asinθ

    Clearly, it passes through (α, 0).

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