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Let S be the quadratic surface given by 2x? + y? – 2z? = 10. (a) Classify S: S is a hyperboloid of two sheets. S is an elliptic paraboloid. S is an elliptic cone. S is an ellipsoid. S is a hyperboloid of one sheet. (b) Find the upward-pointing unit normal N to S at (2, 2, 1). (Write your solution using the standard basis vectors i, j, k. Use symbolic notation and fractions where needed.) N= (c) Find an equation of the tangent plane P to S at the point (2, 2, 1) An equation for P is given by

Let S be the quadratic surface given by 2x? + y? – 2z? = 10. (a) Classify S: S is a hyperboloid of two sheets. S is an elliptic paraboloid. S is an elliptic cone. S is an ellipsoid. S is a hyperboloid of one sheet. (b) Find the upward-pointing unit normal N to S at (2, 2, 1). (Write your solution using the standard basis vectors i, j, k. Use symbolic notation and fractions where needed.) N= (c) Find an equation of the tangent plane P to S at the point (2, 2, 1) An equation for P is given by

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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Let S be the quadratic surface given by 2x? + y? – 2z? = 10. (a) Classify S: S is a hyperboloid of two sheets. S is an elliptic paraboloid. S is an elliptic cone. S is an ellipsoid. S is a hyperboloid of one sheet. (b) Find the upward-pointing unit normal N to S at (2, 2, 1). (Write your solution using the standard basis vectors i, j, k. Use symbolic notation and fractions where needed.) N= (c) Find an equation of the tangent plane P to S at the point (2, 2, 1) An equation for P is given by
Transcribed Image Text:Let S be the quadratic surface given by 2x? + y? – 2z? = 10. (a) Classify S: S is a hyperboloid of two sheets. S is an elliptic paraboloid. S is an elliptic cone. S is an ellipsoid. S is a hyperboloid of one sheet. (b) Find the upward-pointing unit normal N to S at (2, 2, 1). (Write your solution using the standard basis vectors i, j, k. Use symbolic notation and fractions where needed.) N= (c) Find an equation of the tangent plane P to S at the point (2, 2, 1) An equation for P is given by
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