Sphere tangents question, test tomorrow, very important

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SUMMARY

The discussion centers on finding the equation of a sphere with a center at (1, 4, -3) and a radius of √26. The standard equation for a sphere in general form is (x - h)² + (y - k)² + (z - l)² = r², where (h, k, l) is the center and r is the radius. Substituting the given values, the equation becomes (x - 1)² + (y - 4)² + (z + 3)² = 26. The user expresses confusion regarding the relationship between the sphere and a plane, indicating a need for clarification on distance formulas.

PREREQUISITES
  • Understanding of the standard equation of a sphere
  • Knowledge of distance formulas in three-dimensional space
  • Familiarity with coordinate geometry
  • Basic algebra skills for manipulating equations
NEXT STEPS
  • Review the standard equation of a sphere and practice deriving it from given parameters
  • Study the distance formula in three-dimensional space: d = √((x2 - x1)² + (y2 - y1)² + (z2 - z1)²)
  • Explore the relationship between spheres and planes in geometry
  • Practice solving problems involving spheres and their equations
USEFUL FOR

Students preparing for geometry tests, educators teaching coordinate geometry, and anyone needing to understand the properties and equations of spheres.

lolphysics3
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Homework Statement



Find the equation in the general form of the sphere described: Center (1,4,-3) radius square root of 26.

Homework Equations


None


The Attempt at a Solution


Well I need to find the center of the sphere to be able to right the equation. Given the radius, which would be the distance between the center and point on the plane, I thought I could make a system out of it. First equation the distance between the center and the point given (x,y,z) variables, and the distance between the point and the plane equation. I tried to solve it, but it just gave me an equation for a plane that wasn't the solution...Help please? My teacher didn't go over this type of problem or even mention it before today and it's on the test tomorrow.
 
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lolphysics3 said:

Homework Statement



Find the equation in the general form of the sphere described: Center (1,4,-3) radius square root of 26.

Homework Equations


None


The Attempt at a Solution


Well I need to find the center of the sphere to be able to right the equation. Given the radius, which would be the distance between the center and point on the plane, I thought I could make a system out of it. First equation the distance between the center and the point given (x,y,z) variables, and the distance between the point and the plane equation. I tried to solve it, but it just gave me an equation for a plane that wasn't the solution...Help please? My teacher didn't go over this type of problem or even mention it before today and it's on the test tomorrow.

What is the formula for the distance between (x,y,z) and (x',y',z')??
 

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