To sketch the curve, we can rewrite the equation as:
\(\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}+\frac{(z-c)^{2}}{c^{2}}=2\)
This is the equation of an ellipsoid centered at (0, 0, c) with semi-axes lengths a, b, and c. Since z = c, the curve lies on the plane z
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