(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I have a doubt on spheroid equations. A prolate spheroid is obtained by rotating the ellipse,

X^2/a^2 + Y^2/b^2 = 1 {Here a is major axis}

about the semi-major axis a(i.e. X axis). Its equation is,

X^2/a^2 + [Y^2+Z^2]/b^2 = 1

An oblate spheroid is obtained by rotating the ellipse,

X^2/a^2 + Y^2/b^2 = 1 {Here b is major axis}

about the semi-minor axis a(i.e. X axis).Its equation is,

X^2/a^2 + [Y^2+Z^2]/b^2 = 1

The problem is that both equations are identical. What I have done is that I have taken ‘a’ always along X axis and ‘b’ always along Y axis. Is it necessary that the equations be distinguishable?

2. Relevant equations

X^2/a^2 + Y^2/b^2 = 1

3. The attempt at a solution

In order distinguish between the two, I will have to take ‘a’ along Y axis for one of them. Suppose I take ‘a’ along the Y axis for oblate spheroid case, the equation of the oblate spheroid is got by rotating the ellipse,

X^2/b^2 + Y^2/a^2 = 1

about the semi-minor axis ‘b’(i.e. X axis).Its equation is,

X^2/b^2 + [Y^2+Z^2]/a^2 = 1

Another way is to rotate the ellipse,

X^2/a^2 + Y^2/b^2 = 1 {Here a is major axis}

first along X axis(i.e. ‘a’) for prolate spheroid in which case the equation becomes,

X^2/a^2 + [Y^2+Z^2]/b^2 = 1

And then along Y axis(i.e. ‘b’) for oblate spheroid in which case the equation becomes,

[X^2+Z^2]/a^2 + Y^2/b^2 = 1 {Here b is major axis}

Is there a better way to this? Please help.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Equation of spheroid

**Physics Forums | Science Articles, Homework Help, Discussion**