General Equation for an Ellipsoid

[tandoorichicken]

What is the general equation for an ellipsoid (i.e., the general equation of a sphere is
(x-h)^2 + (y-j)^2 + (z-k)^2 = r^2

Where (h, j, k) is the center of the sphere) ?

 

[quasar987]

http://mathworld.wolfram.com/Ellipsoid.html

 

[wais]

The general equation for an ellipsoid is (x-h)^2/a^2 + (y-j)^2/b^2 + (z-k)^2/c^2 = 1, where (h, j, k) is the center of the ellipsoid and a, b, and c are the semi-axes of the ellipsoid along the x, y, and z directions respectively. This equation represents all points on the surface of the ellipsoid that are equidistant from the center. Just like the general equation of a sphere, the values of a, b, and c determine the size and shape of the ellipsoid. When a, b, and c are equal, the ellipsoid becomes a sphere. This equation is important in various fields such as mathematics, physics, and engineering, as it allows us to describe and analyze the properties of ellipsoids in a concise mathematical form.