Question

Sketch an accurate graph of the surface whose equation is

4x²+y²+z²=16. Find the traces in each of the coordinate planes, and use the traces to sketch the
surface. Use an appropriate scale and includeintercepts on the x, y, and z axes. Name the surface.

Answer 1

To sketch the graph of the surface 4x²+y²+z²=16, we can find the traces in each coordinate plane and use them to sketch the surface as a sphere.

Step-by-step explanation:

To sketch the graph of the surface given by the equation 4x²+y²+z²=16, we can start by finding the traces in each of the coordinate planes.

For the xy-plane (z=0), the equation becomes 4x²+y²=16, which is a circle with radius 4 centered at the origin.

For the xz-plane (y=0), the equation becomes 4x²+z²=16, which is another circle with radius 4 centered at the origin.

For the yz-plane (x=0), the equation becomes y²+z²=16, which is a circle with radius 4 centered at the origin.

By using the traces in each plane, we can sketch the surface. The surface represented by the given equation is a sphere centered at the origin with radius 4.