Supose a planet is revolving around the sun in an elliptical path given by `(x^(2))/(a^(2)) + (y^(2))/(b^(2))=1`
Find time period of revolution Angular momentum of the planet about the sun is `L`
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Explanation

Rate of area swept `(dA)/(dt) = (L)/(2m)` =constant
`rArr dA = L/(2m)dt`
`underset(A=0)overset(A=piab)intdA=underset(t=0)overset(t=T)int(L)/(2m)dt`
`rArrpiab=(L)/(2m)TrArrT=(2pimab)/(L)` .