Question

Please help me get started on the following problem. Find an equation of the sphere with center (2,-1,-3) satisfying the given condition: Tangent to the xy-plane.

Answer 1

If I recall correctly, a sphere with center \((h,k,l)\) has the equation
\[r^2=(x-h)^2+(y-k)^2+(z-l)^2,\]
where \(r\) is the radius of the sphere.

You know the center, so you just have to find the radius of the sphere. It's tangent to the xy-plane, so you have to find the distance from the center (2,-1,-3) to this point's projection on the xy-plane, which would be (2, -1, 0).

Answer 2

How did you determine the point (2,-1,0)?

Answer 3

Forgive the poor drawing. It's a bit tough in three dimensions.