Standard Equation of Ellipsoid

Theorem

Let $\EE$ be an ellipsoid whose axes of symmetry coincide with the coordinate axes of a Cartesian $3$-space.

Then $\EE$ can be expressed by the equation:

$\dfrac {x^2} {a^2} + \dfrac {y^2} {b^2} + \dfrac {z^2} {c^2} = 1$

Proof

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Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): ellipsoid
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): ellipsoid