(1 point) Answer the following questions about the sphere whose equation is given by x2+y2+z2−4x+4y=73. x2+y2+z2−4x+4y=73. 1. Find the radius of the sphere. Radius: r=r= 2. Find the center of the sphere. Write the center as a point (a, b,c)(a, b,c) where aa, bb, and cc are numbers.

R=9.

C=(2,-2,0).

Explanation:

Lets try to find how can be written in the form of , since then its radius R and center of coordinates C=(a,b,c) would be easily recognizable.

Since we have the terms -4x and +4y, they seem to have come from the terms and , and we would need to take care of the extra +4 by substracting then. More explicitly:

, as we had originally with the x terms

, as we had originally with the y terms

Which means:

Or, putting all together:

So our radius is 9 and the center is (2,-2,0).

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