Intersection of a circle with coordinate planes

[Calpalned]

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 X² + Y² + Z² = R²

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?

 

[Borg]

Since one of your starting points (-6) is farther from an axis than the radius of the sphere (5), it seems reasonable that the sphere wouldn't intersect with one of the planes.

 

[Calpalned]

Since one of your starting points (-6) is farther from an axis than the radius of the sphere (5), it seems reasonable that the sphere wouldn't intersect with one of the planes.

Thanks Borg. I never noticed the correlation between the points and the radius before.