Question

Use traces to sketch the surface. 6x² − y²+ z² = 0 WebAssign Plot WebAssign Plot WebAssign Plot WebAssign Plot Identify the surface. elliptic paraboloid hyperboloid of two sheets hyperbolic paraboloid ellipsoid elliptic cone parabolic cylinder hyperboloid of one sheet elliptic cylinder.

Answer 1

The equation 6x² - y² + z² = 0 represents an ellipsoid. To sketch the surface, we can use traces, which are the intersections of the surface with planes parallel to the coordinate planes.

Step-by-step explanation:

The equation 6x² - y² + z² = 0 represents an ellipsoid. To sketch the surface, we can use traces.

A trace is the intersection of the surface with a plane that is parallel to one of the coordinate planes (x, y, or z).

For example, if we set x = 0, we get -y² + z² = 0, which is a circle in the yz-plane.

Similarly, setting y = 0 gives us 6x² + z² = 0, which is an ellipse in the xz-plane.

Setting z = 0 results in 6x² - y² = 0, which is another ellipse in the xy-plane.

By analyzing the traces in each plane, we can sketch the overall shape of the ellipsoid.