Thread: Intersection of a sphere with xz plane

Find an equation of the sphere with center (1,-4,3) and
radius 5. What is the intersection of this sphere with the xz-plane?

I know that the equation would be:


and the intersection would be

but how do you determine the radius of the intersecting circle?

Any help is greatly appreciated

For all points on the xz plane, y is zero. Since these points must also be on the sphere, you just need to set y to 0 in your equation for the sphere and that will give you the equation of the circle of intersection.