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Question
If x and y are connected parametrically by the equations, without eliminating the parameter, find `bb(dy/dx)`.
x = a (θ – sin θ), y = a (1 + cos θ)
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Solution
Here x = a (θ – sin θ) ...(1)
y = a (1 + cos θ) ...(2)
Differentiating (1) and (2) w.r.t. θ, we get
`dx/(dθ)` = a [1 – cos θ]
`dy/(dθ)` = a [–sin θ]
= –a sin θ
`dy/dx = (dy/(dθ))/(dx/(dθ))`
= `(-a sin θ)/(a (1 - cos θ))`
= `(- sin θ)/(1- cos θ)`
= `(-2 sin θ //2 cos θ//2)/(2 sin^2 θ//2)`
= `-cot θ/2`
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