If `x=asint-bcost ,\ \ y=acost+bsint` , prove that `(d^2y)/(dx^2)=-(x^2+y^2)/(y^3)` .

Explanation

`x=a sin t-b cos t, y=a cos t+b sin t`

On differentiating with respect to t, we get
`
frac{d x}{d t}=frac{d}{d t}(a sin t-b cos t)=a cos t+b sin t`

and
`
frac{d y}{d t}=frac{d}{d t}(a cos t+b sin t)=-a sin t+b cos t`

Now,` (frac{d y}{d x})=frac{frac{d y}{d t}}{frac{d x}{d t}}=frac{-a sin t+b cos t}{a cos t+b sin t}`

Therefore,
`

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