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Hyperbolic paraboloid: (a) What does the horizontal cross section given by z = 0 look like? Check on the first picture, and also look at the equation when z = 0. Is this still a hyperbola? (b) How would z = y²-2² look different than z = r² - y²?

Hyperbolic paraboloid: (a) What does the horizontal cross section given by z = 0 look like? Check on the first picture, and also look at the equation when z = 0. Is this still a hyperbola? (b) How would z = y²-2² look different than z = r² - y²?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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The basic hyperbolic paraboloid is given by the equation where A and B have opposite signs. With just the flip of a sign, say z = Az² + By³ 2²+y² to 2²-² we can change from an elliptis paraboloid to a much more complex surface. Because it's such a neat surface, with a fairly simple equation, we use it over and ever in examples. Hyperbolic paraboloids are often referred to as "saddles", for fairly obvious reasons. Their official name stems from the fact that their vertical cross sections are parabolas, while the horizontal cross sections are hyperbolas. But even the vertical cross sections are more complicated than with an elliptic paraboloid. Look at the picture below, which shows the surface 2-2²-²
Transcribed Image Text:The basic hyperbolic paraboloid is given by the equation where A and B have opposite signs. With just the flip of a sign, say z = Az² + By³ 2²+y² to 2²-² we can change from an elliptis paraboloid to a much more complex surface. Because it's such a neat surface, with a fairly simple equation, we use it over and ever in examples. Hyperbolic paraboloids are often referred to as "saddles", for fairly obvious reasons. Their official name stems from the fact that their vertical cross sections are parabolas, while the horizontal cross sections are hyperbolas. But even the vertical cross sections are more complicated than with an elliptic paraboloid. Look at the picture below, which shows the surface 2-2²-²
2. Hyperbolic paraboloid: (a) What does the horizontal cross section given by z = 0 look like? Check on the first picture, and also look at the equation when z = 0. Is this still a hyperbola? (b) How would z = y²-2² look different than z = 2² - y²?
Transcribed Image Text:2. Hyperbolic paraboloid: (a) What does the horizontal cross section given by z = 0 look like? Check on the first picture, and also look at the equation when z = 0. Is this still a hyperbola? (b) How would z = y²-2² look different than z = 2² - y²?
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