Quandaries and Queries 

Name: jaidev Who is asking: Student Question: Is there any general equation for a sphere? Hi Jaidev, I expect you know that the equation of the circle of radius r, centered at the origin, is The point (x,y) is on the circle if and only if the right triangle with legs of length x and y has hypotenuse of length r, that is
For a sphere you need to use Pythagoras' theorem twice. In the diagram below O is the origin and P(x,y,z) is a point in 3space. P is on the sphere with center O and radius r if and only if the distance from O to P is r.
The triangle OAB is a right triangle and hence x^{2} + y^{2} = s^{2}. The triangle OBP is also a right triangle and hence s^{2} + z^{2} = r^{2}. Hence the distance OP from O to P satisfies Similarly (x,y,z) is on the sphere with center (h,j,k) and radius r if and only if 

