1. ## sphere

On the sphere x squared + y squared +z squared=13squared, there are many great circles that intersect at (3,4-12). Find coordinates for the other points where these circles all intersect.

i am not sure I understand this problem.

2. ## Re: sphere

Do you know the definition of a 'great circle'?

3. ## Re: sphere

Hello, Veronica1999!

On the sphere $\displaystyle x^2+y^2+z^2\:=\:13^2$
. . there are many great circles that intersect at $\displaystyle (3,4-12).$
Find coordinates for the other points where these circles all intersect.

i am not sure I understand this problem.

Consider the planet Earth.
There are many circles of longitude (which are all great circles)
. . from the Prime Meridian to the International Date Line.
They all intersect at the North Pole and the South Pole.

We are given a sphere.
The point (3, 4, -12) is a "pole" of this globe.
The other pole is diametrically opposite.
Where is it?

China.

5. ## Re: sphere

Then it would be (-3, -4, 12) ?

Right!