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x² = y² + 4z²

x² = y² + 4z²

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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is 1 plane through the line of intersection of plane x + y - 2z = 1. the planes x -z = 1 and y + 2z = 3 and perpendicular to the 26. (a) Find an equation of the plane that passes through the points A(2, 1, 1), B(-1,-1, 10), and C(1, 3, -4). (b) Find symmetric equations for the line through B that is perpendicular to the plane in part (a). (c) A second plane passes through (2, 0, 4) and has normal vector (2, -4, -3). Show that the acute angle between the planes is approximately 43°. (d) Find parametric equations for the line of intersection of the two planes. 27. Find the distance between the planes 3x + y - 4z = 2 and 3x + y - 4z = 24. 28-36 Identify and sketch the graph of each surface. 28. x = 3oldad: 1 29. x = Z ali 31. x² = y² + 4z² MUDI 33. -4x² + y² - 4z² = 4 30. y = z² ted 32. 4x - y + 2z = 4 34. y² + z² = 1 + x² 35. 4x² + 4y² - 8y + z² = 0 36. x = y² + z² - 2y - 4z + 5 37. An ellipsoid is created by rotating the ellipse 4x² + y² = 16 about the x-axis. Find an equation of the ellipsoid. 38. A surface consists of all points P such that the distance from P to the plane y = 1 is twice the distance from P to the point (0, -1,0). Find an equation for this surface and identify it.
Transcribed Image Text:is 1 plane through the line of intersection of plane x + y - 2z = 1. the planes x -z = 1 and y + 2z = 3 and perpendicular to the 26. (a) Find an equation of the plane that passes through the points A(2, 1, 1), B(-1,-1, 10), and C(1, 3, -4). (b) Find symmetric equations for the line through B that is perpendicular to the plane in part (a). (c) A second plane passes through (2, 0, 4) and has normal vector (2, -4, -3). Show that the acute angle between the planes is approximately 43°. (d) Find parametric equations for the line of intersection of the two planes. 27. Find the distance between the planes 3x + y - 4z = 2 and 3x + y - 4z = 24. 28-36 Identify and sketch the graph of each surface. 28. x = 3oldad: 1 29. x = Z ali 31. x² = y² + 4z² MUDI 33. -4x² + y² - 4z² = 4 30. y = z² ted 32. 4x - y + 2z = 4 34. y² + z² = 1 + x² 35. 4x² + 4y² - 8y + z² = 0 36. x = y² + z² - 2y - 4z + 5 37. An ellipsoid is created by rotating the ellipse 4x² + y² = 16 about the x-axis. Find an equation of the ellipsoid. 38. A surface consists of all points P such that the distance from P to the plane y = 1 is twice the distance from P to the point (0, -1,0). Find an equation for this surface and identify it.
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