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If x=asin(pt), y=bcos(pt), then show tha...

If `x=asin(pt)`, `y=bcos(pt)`, then show that `(a^2-x^2)y(d^y)/(dx^2)+b^2=0`

Text Solution

Verified by Experts

`x = asin(pt)`
`=>dx/dt = apcospt`
`y = bcospt`
`dy/dt = -bp sinpt`
`:. dy/dx = -(bp sinpt)/(apcospt) = -b/atanpt`
`=>(d^2y)/dx^2 = -b/a (sec^2pt) (p) dt/dx`
As `dx/dt = apcospt`
`:. dt/dx = 1/(ap) secpt`
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