Question

Use traces to sketch the surface. −x²+ 5y² − z²= 5
Identify the surface

Answer 1

To sketch the surface represented by the equation -x² + 5y² - z² = 5, we can use traces. Traces involve fixing the values of one variable and solving for the others. The resulting traces can be connected to form a visualization of the surface.

Step-by-step explanation:

To sketch the surface represented by the equation -x² + 5y² - z² = 5, we can use traces. Traces are the curves resulting from holding one variable constant while allowing the others to vary. We'll sketch traces by fixing the values of z and solving for x and y.

1. When z is held constant at 0, the equation becomes -x² + 5y² = 5. This represents an ellipse with its major axis along the y-axis.
2. When y is held constant at 0, the equation becomes -x² - z² = 5. This represents a hyperbola in the xz-plane.
3. When x is held constant at 0, the equation becomes 5y² - z² = 5. This represents another hyperbola in the yz-plane.

By sketching these traces and connecting them, we can visualize the surface.