if x=acost+bsint and y=asint-bcost show that y^2y2-xy1 +y=0
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x= acost +bsint ----(1)
y = asint - bcost--(2)
do square of (1) and (2)
x² = a²cos²t +b²sin²t +2abcostsint ---(3)
y²= a²sin²t +b²cos²t - 2ab cost sint---(4)
add (3) and (4)
x²+y² = a²(cos²t +sin²t) +b²(sin²t+cos²t)
x²+y²= a²+b² [ ∵ cos²t +sin²t =1]
x= acost +bsint ----(1)
y = asint - bcost--(2)
do square of (1) and (2)
x² = a²cos²t +b²sin²t +2abcostsint ---(3)
y²= a²sin²t +b²cos²t - 2ab cost sint---(4)
add (3) and (4)
x²+y² = a²(cos²t +sin²t) +b²(sin²t+cos²t)
x²+y²= a²+b² [ ∵ cos²t +sin²t =1]
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