If x = 3cos t and y = 5sin t , where t is a parameter, then 9 d ^ 2...

\dfrac{dy}{dx} = \dfrac{\dfrac{dy}{dt}}{\dfrac{dx}{dt}} = \dfrac{5cos t}{- 3sin t} = \dfrac{- 5}{3}\cot \left(t\right)$<br />$\dfrac{{d}^{2}y}{d{x}^{2}} = \dfrac{- 5}{3} ⋅ \left(- cose{c}^{2}t\right) ⋅ \dfrac{dt}{dx} = \dfrac{5}{3}\left(\dfrac{1}{\sin^{2} t}\right)\left(\dfrac{1}{- 3sin t}\right)$<br />$= \dfrac{5}{9}\left(8\right)