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**1. The problem statement, all variables and given/known data**

Describe and sketch the geometric objects represented by the

systems of equations

**2. Relevant equations**

x

^{2}+ y

^{2}+ z

^{2}= 4

x + y + z = 1

**3. The attempt at a solution**

I can sketch both objects:

1) sphere with center (0,0,0) and radius 2

2) "simple" plane with intersection points (on xyz plane): (1,0,0), (0,1,0), (0,0,1)

I see that their intersection will give us the circle.

However, I

__cant guess the center and the radius.__

what I tried on this issue so far:

from eq. 2 ->

**z = 1 - (x +y)**and put it in eq.1

we get (after few steps):

x

^{2}+ y

^{2}+ xy - x - y = 3/2

It's really hard to guess all the mentioned parameters, considering that it doesn't have the circle equation form: x

^{2}+ y

^{2}= k (which is understandable, cause it on a "tilted" plane)

Any ideas, how to guess the mentioned variables, or change the equation in to "better" form?