Worksheet: Quadratic Surfaces in Three Dimensions

In this worksheet, we will practice identifying the equations and graphs of quadratic surfaces in 3D such as cylinders, cones, ellipsoids, hyperboloids, and paraboloids.

Q1:

Find the trace of the hyperboloid of one sheet 𝑥𝑎+𝑦𝑏𝑧𝑐=1 in the plane 𝑥=𝑎 and in the plane 𝑦=𝑏.

  • A𝑥𝑎=𝑧𝑐 and 𝑦𝑏=𝑧𝑐
  • B𝑥𝑎+𝑦𝑏=1 and 𝑧=0
  • C𝑥𝑎=𝑧𝑐 and 𝑦𝑏=𝑧𝑐
  • D𝑥𝑎=𝑧𝑐 and 𝑦𝑏=𝑧𝑐
  • E𝑥𝑎=𝑧𝑐 and 𝑦𝑏=𝑧𝑐

Q2:

Find the trace of the hyperbolic paraboloid 𝑥𝑎𝑦𝑏=𝑧𝑐 in the 𝑥𝑦-plane.

  • A𝑥𝑎=𝑦𝑏 and 𝑧=0
  • B𝑥𝑎=𝑦𝑏 and 𝑧=1
  • C𝑥𝑎=𝑦𝑏 and 𝑧=0
  • D𝑥𝑎=𝑦𝑏 and 𝑧=1
  • E𝑥𝑎=𝑦𝑏 and 𝑧=0

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.