Question

Use an equation to describe the intersection of the sphere with each of the coordinate planes. If the sphere does not intersect with the plane, enter DNE.

Answer 1

The intersection of a sphere with a coordinate plane can be described using equations.

Step-by-step explanation:

When a sphere intersects with a coordinate plane, the coordinates of the points of intersection can be described using equations. For example, if the sphere intersects with the xy-plane, then the z-coordinate of the points of intersection will be zero. So the equation for the intersection of the sphere with the xy-plane is z = 0. Similarly, if the sphere intersects with the xz-plane, the y-coordinate of the points of intersection will be zero, so the equation is y = 0. If the sphere intersects with the yz-plane, the x-coordinate of the points of intersection will be zero, so the equation is x = 0.