Learn how to find the equation of a sphere given a center point and radius in 3D. We will then find the intersection of the sphere with the yz-plane. Three-Dimensional Coordinate Systems is the first topic in a typical Calculus 3 (multivariable calculus) course. 3D coordinates provide a method to graph and explore vectors, vector functions, multivariable functions, and many applications.
Book: Calculus: Early Transcendentals 8th Edition by James Stewart
Current Topic: 12.1 Three-Dimensional Coordinate Systems
(1-6 Calculus 1 | 7-11 Calculus 2 | 12-16 Calculus 3)
1. Functions and Models
2. Limits and Derivatives
3. Differentiation Rules
4. Applications of Differentiation
5. Integrals
6. Applications of Integration
7. Techniques of Integration
8. Further Applications of Integration
9. Differential Equations
10. Parametric Equations and Polar Coordinates
11. Infinite Sequences and Series
12. Vectors and Geometry of Space
12.1: Three-Dimensional Coordinate Systems
12.2: Vectors
12.3: The Dot Product
12.4: The Cross Product
12.5: Equations and Planes
12.6: Cylinders and Quadric Surfaces
Review
13. Vector Functions
14. Partial Derivatives
15. Multiple Integrals
16. Vector Calculus
17. Second-Order Differential Equations
Question:
13. Find an equation of the sphere with center (-3, 2, 5) and radius 4. What is the intersection of this sphere with the yz-plane?
Question Copy Pasted:
13. Find an equation of the sphere with center s23, 2, 5d and radius 4. What is the intersection of this sphere with the yz-plane?
20 авг 2024
