Question

If x and y are connected parametrically by the equation, without eliminating the parameter, find dy/dx x = a cos θ, y = b cos θ

Answer 1

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Answer 2

Given, $\bf{x=acos\theta\:,\:y=bcos\theta}$

$\bf{\underline{x=acos\theta}}$
now differentiate x with respect to θ
dx/dθ = a. d(cosθ)/dθ = a. (-sinθ)
dx/dθ = -asinθ ------(1)

$\bf{\underline{y=bcos\theta}}$
now differentiate y with respect to θ
dy/dθ = b. d(-sinθ)/dθ = b. ( -sinθ)
dy/dθ = -bsinθ -----(2)

dividing equations (2) by (1)
{dy/dθ}/{dx/dθ} = (-bsinθ)/(-asinθ)
dy/dx = $\bf{\frac{b}{a}}$