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Newtonian Mechanics

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Question 1 of 5

The Hamiltonian of a particle of unit mass moving in the xy plane is given to be $H = xP _{ x }- yP _{ y }-1 / 2 x ^{2}+1 / 2 y ^{2}$ in suitable units , The initial values are given to be and $\left( P _{ x }(0), P _{ y }(0)\right)=(1 / 2,-1 / 2)$ During the motion , the curved traced out by the particles in the xy - plane and the PxPy - plane are

A

A hyperbola and an ellipse, respectively

B

Both hyperbolas

C

Both straight lines

D

A straight line and a hyperbola respectively