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## Homework Statement

Find an equation of the sphere with center (2, -6, 4) and radius 5. Describe its intersection with the each of the coordinate planes.

## Homework Equations

Equation of a sphere with three dimensions X

^{2}+ Y

^{2}+ Z

^{2}= R

^{2}

## The Attempt at a Solution

My equation is (x - 2)

^{2}+ (y + 6)

^{2}+ (z - 4)

^{2}= 25

This sphere intersects the XY plane by making a circle with radius 3 and it intersects the YZ plane with a radius of (21)

^{0.5}. However, my equation for the XZ plane came out to be negative. That is, Radius squared is less than zero. Does that mean the sphere doesn't intersect the XZ plane?