With the z-axis vertical a sphere has center 2 3 7 and

Question

Question: 1. With the z-axis vertical, a sphere has center (2, 3, 7) and lowest point (2, 3, -1). What is the highest point on the sphere?

2. Find the equations of planes that just touch the sphere (x- 2)² + (y - 3)² + (z - 3)² = 16 and are parallel to

(a) The xy-plane

(b) The yz-plane

(c) The xz-plane