Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Suppose we have a sphere with radius $3$ centered at $(-3,3,2)$. What is the equation of the trace of this sphere on the $xy$ plane?

share|cite|improve this question
Write down the equation of the sphere. Intersect it with $xy$ by substituting $z = 0$. You'll get a circle of center $(-3, 3, 0)$ and radius $\sqrt{5}$. The projection of the sphere is concentric but has bigger radius: $3$. – user2468 Aug 29 '12 at 15:53

Hint: The center projected onto the $xy$-plane is $(-3,3,0)$. So you get a circle of radius $3$ with that center.

share|cite|improve this answer

It is described by equations of a circle of radius $3$ and the center in $(-3,3,0)$ contained in the plane $XY$. So it is:

$$(x+3)^2+(y-3)^2=9\ \ \ \mbox{and}\ \ \ z=0.$$

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.