an of a 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. Find equations of the spheres with center (2, -3, 6) that touch (a) the xy-plane, (b) the yz-plane, (c) the xz-plane. 24. Find an equation of the largest sphere with center (5, 4, 9) that is contained in the first octant. 25-38 Describe in words the region of R³ represented by the equation(s) or inequality. 25. x = 5 27. y < 8 29.0≤z≤6 31. x² + y² = 4, z = -1 33. x² + y² + z² = 4 35. 1 ≤ x² + y² + z²¹ < 5 37. x² + z² ≤ 9 26. y = -2 28. z > -1 30. y² = 4 32. x² + y² = 4 34. x² + y² + z²<4 36. x = z 38. x² + y² + z² > 2z 39-42 Write inequalities to describe the region. 39. The region between the yz-plane and the vertical plane x = 5

an of a 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. Find equations of the spheres with center (2, -3, 6) that touch (a) the xy-plane, (b) the yz-plane, (c) the xz-plane. 24. Find an equation of the largest sphere with center (5, 4, 9) that is contained in the first octant. 25-38 Describe in words the region of R³ represented by the equation(s) or inequality. 25. x = 5 27. y < 8 29.0≤z≤6 31. x² + y² = 4, z = -1 33. x² + y² + z² = 4 35. 1 ≤ x² + y² + z²¹ < 5 37. x² + z² ≤ 9 26. y = -2 28. z > -1 30. y² = 4 32. x² + y² = 4 34. x² + y² + z²<4 36. x = z 38. x² + y² + z² > 2z 39-42 Write inequalities to describe the region. 39. The region between the yz-plane and the vertical plane x = 5

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter10: Analytic Geometry

Section10.1: The Rectangular Coordinate System

Problem 44E: By definition, a hyperbola is the locus of points whose positive difference of distances from two...

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