Prove that cuts in the ambiguity function are always defined by an ellipse. Hint: approximate the ambiguity

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Prove that cuts in the ambiguity function are always defined by an ellipse. Hint: approximate the ambiguity function using a Taylor series expansion about the values (τ,fd)=(0,0); use only the first three terms in the Taylor series expansion.
The radar uncertainty principle establishes a lower bound for the time bandwidth product. More specifically, if the radar effective duration is τe, and its effective bandwidth is Be, show that Be2τe2(1ρRDC2)π2, where ρRDC is the range-Doppler coupling coefficient defined in Chapter 4.

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