quadric surfaces cheat sheet, Cheat Sheet of Mathematics

Download quadric surfaces cheat sheet and more Cheat Sheet Mathematics in PDF only on Docsity! Quadric Surface Examples Example 1 (12.6.30). 4x2 − y + 2z2 = 0 ⇔ y = x 2 1/4 + z2 1/2 This is a paraboloid with vertex at the origin, opening along the y-axis. Figure 1: Paraboloid Example 2 (12.6.36). x2 − y2 + z2 − 2x + 2y + 4z + 2 = 0 ⇔ (x− 1) 2 2 − (y − 1) 2 2 + (z + 2)2 2 = 1 This is a hyperboloid of one sheet centered at (1, 1,−2). Figure 2: Hyperboloid of one sheet 1 Example 3 (12.6.15). −x2 + 4y2 − z2 = 4 ⇔ This is a hyperboloid of two sheets centered at the origin. Figure 3: Hyperboloid of two sheets Example 4 (12.rev.35). 4x2 + 4y2 − 8y + z2 = 0 ⇔ This is an ellipsoid centered at (0, 1, 0). Figure 4: Ellipsoid 2