SUMMARY
The equation of a sphere centered at (-7, 6, 7) with a radius of 2 is derived from the standard formula (x - x₀)² + (y - y₀)² + (z - z₀)² = r². Substituting the center and radius, the equation becomes (x + 7)² + (y - 6)² + (z - 7)² = 4. Normalization in this context means ensuring the coefficient of x² is 1, which is already satisfied in the derived equation. The final normalized equation is (x + 7)² + (y - 6)² + (z - 7)² = 4.
PREREQUISITES
- Understanding of multivariable calculus concepts
- Familiarity with the equation of a sphere
- Knowledge of algebraic manipulation
- Ability to normalize equations
NEXT STEPS
- Study the derivation of the equation of a sphere in three-dimensional space
- Learn about normalization techniques in algebra
- Explore applications of spheres in multivariable calculus
- Practice solving similar problems involving spheres and their equations
USEFUL FOR
Students studying multivariable calculus, educators teaching geometry, and anyone looking to enhance their understanding of spherical equations and normalization techniques.