Let the isotherms (curves of constant temperature) in a body in the upper half-plane y > 0

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Let the isotherms (curves of constant temperature) in a body in the upper half-plane y > 0 be given by 4x2 + 9y2 = c. Find the orthogonal trajectories (the curves along which heat will flow in regions filled with heat-conducting material and free of heat sources or heat sinks).

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