# QuadricsHomework - Homework 4 February 11th The following...

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Homework 4 – February 11th The following are questions about the Interactive Gallery of Quadric Surfaces which can be found at http://www.math.uiuc.edu/Courses/math241/quadrics/index.html . 1. On the page titled “Interactive Gallery of Quadric Surfaces” [get there by clicking “Home” in the navigation panel] there are 5 equations. (a) By browsing the other pages in the interactive gallery, identify the general equation with each quadric surface is represented. (b) What changes in the general equation z = Ax 2 + By 2 to diﬀerentiate between a hyper- bolic paraboloid and an elliptic paraboloid. 2. Click on “Elliptic Paraboloid” in the navigation panel. (a) By sliding the blue dots back and forth along the appropriate axes, determine the shape of the cross-sections of the elliptic paraboloid x 2 + y 2 = z in the planes x = 0 ,y = 0 and z = 0. (b) Describe why this surface is called a paraboloid. Additionally, why should this surface be referred to as a circular paraboloid, rather than an elliptic paraboloid. (c) On the second (lower) illustration, change the values to be

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QuadricsHomework - Homework 4 February 11th The following...

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