Final answer:
To find the equation of a sphere with a center that is tangent to the xz-plane, use the coordinates of the center and the radius of the sphere. The equation of the sphere is x^2 + (y - R)^2 + z^2 = R^2.
Step-by-step explanation:
To find the equation of a sphere with a center that is tangent to the xz-plane, we need to determine the coordinates of the center. Since the center is tangent to the xz-plane, the y-coordinate of the center would be the radius of the sphere. Let's denote the center as (a, R, b), where R is the radius of the sphere. The equation of the sphere can be written as:
(x - a)^2 + (y - R)^2 + (z - b)^2 = R^2
Since the center is tangent to the xz-plane, the y-coordinate of the center is equal to the radius of the sphere, which means a = b = 0. So the equation of the sphere is:
x^2 + (y - R)^2 + z^2 = R^2