Ellipsoid

Ellipsoid: -

A is represent to x-axis and b is represent to y and c represents to z-axis
An ellipse surface will be described as an extension of a spherical surface wherever the radii in 3 mutually perpendicular directions will have a special value. The cartesian representation for points over the surface of an ellipsoid focused on the origin is
\[\frac{x^2}{a^2}+ \frac{y^2}{b^2} +\frac{z^2}{c^2}=1\]

Torus: -

A Torus is a doughnut shape object shown in the figure
It can be generated by rotating a circle or other conic object about a specified an axis. The Cartesian representation the for points over the surface or a torus can be return in the form

\[r-\sqrt{\frac{x^2}{a^2}+\frac{y^2}{b^2}}+\frac{z^2}{c^2}=1\]

Where a,b,c is the value from origin 0 to axis x,y,z respectively and r is the radius of a given surface.

Elliptic Cylinder: -

With the help of given ellipse we can create a cylinder with x-axis or y-axis or z-axis represented by

\[\frac{x^2}{a^2}+ \frac{y^2}{b^2}=1\]

Similarly, y-z plane

\[\frac{y^2}{b^2}+ \frac{z^2}{c^2}=1\]

And z-x plane

\[\frac{x^{2}}{a^{2}}+\frac{z^{2}}{c^2} = 1\]

Elliptic cone: -

With the equation \[\frac{x^2}{a^2}+ \frac{y^2}{b^2}={z^2}\] can represent elliptic cone where a=b=r we have a right circular cone.