Question

Sketch or describe the surfaces in R^3 of the equations presented.

1. 4x ² + y ² = 16
2. x/4 = y ² /4 + z2/9
3. 4x ² - 3y ² + 2z2 = 0
4. x2/9 + y2/12 + z2/9 = 1

Answer 1

The given equations describe different surfaces in three-dimensional space.

Step-by-step explanation:

The given equations describe surfaces in three-dimensional space. Let's analyze each equation:

1. 4x² + y² = 16 represents an elliptical cylinder aligned with the z-axis.
2. x/4 = y²/4 + z²/9 represents a paraboloid opening towards the positive x-axis.
3. 4x² - 3y² + 2z² = 0 represents a hyperboloid of one sheet.
4. x²/9 + y²/12 + z²/9 = 1 represents an ellipsoid centered at the origin.