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19. 2x² + 2y² + 2z² = 8x - 24z + 1

19. 2x² + 2y² + 2z² = 8x - 24z + 1

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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13. Find an yz-plane? radius 4. What is the intersection of this sphere with the sphere with center (-3, 2, 5) and 14. Find an equation of the sphere with center (2, -6, 4) and radius 5. Describe its intersection with each of the coordinate planes. (4, 3, -1) and has center (3, 8, 1). 15. Find an equation of the sphere that passes through the point 16. Find an equation of the sphere that passes through the origin and whose center is (1, 2, 3). center and radius. 17-20 Show that the equation represents a sphere, and find its 17. x² + y² + z² - 2x - 4y + 8z = 15 18. x² + y² + z² + 8x - 6y + 2z + 17 = 0 19. 2x² + 2y² + 2z² = 8x - 24z + 1 20. 3x² + 3y² + 3z² = 10 + 6y + 12z 21. (a) Prove that the midpoint of the line segment from P₁(x₁, y₁, Z₁) to P₂(x2, y2, 22) is ZI x₁ + x₂ y₁ + y₂ 2₁ +22 2 2 2 (b) Find the lengths of the medians of the triangle with ver- tices A(1, 2, 3), B(-2, 0, 5), and C(4, 1, 5). (A median of a triangle is a line segment that joins a vertex to the midpoint of the opposite side.) 22. Find an equation of a sphere if one of its diameters has end- points (5, 4, 3) and (1, 6, -9). 23. for (2, -3, 6) that touch CTION 12 40. The solic or above radius 2 41. The regi spheres 42. The soli at the or 43. The fig which i the poin on L₁.) (a) Fir (b) Lo the Cons
Transcribed Image Text:13. Find an yz-plane? radius 4. What is the intersection of this sphere with the sphere with center (-3, 2, 5) and 14. Find an equation of the sphere with center (2, -6, 4) and radius 5. Describe its intersection with each of the coordinate planes. (4, 3, -1) and has center (3, 8, 1). 15. Find an equation of the sphere that passes through the point 16. Find an equation of the sphere that passes through the origin and whose center is (1, 2, 3). center and radius. 17-20 Show that the equation represents a sphere, and find its 17. x² + y² + z² - 2x - 4y + 8z = 15 18. x² + y² + z² + 8x - 6y + 2z + 17 = 0 19. 2x² + 2y² + 2z² = 8x - 24z + 1 20. 3x² + 3y² + 3z² = 10 + 6y + 12z 21. (a) Prove that the midpoint of the line segment from P₁(x₁, y₁, Z₁) to P₂(x2, y2, 22) is ZI x₁ + x₂ y₁ + y₂ 2₁ +22 2 2 2 (b) Find the lengths of the medians of the triangle with ver- tices A(1, 2, 3), B(-2, 0, 5), and C(4, 1, 5). (A median of a triangle is a line segment that joins a vertex to the midpoint of the opposite side.) 22. Find an equation of a sphere if one of its diameters has end- points (5, 4, 3) and (1, 6, -9). 23. for (2, -3, 6) that touch CTION 12 40. The solic or above radius 2 41. The regi spheres 42. The soli at the or 43. The fig which i the poin on L₁.) (a) Fir (b) Lo the Cons
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