The discussion focuses on finding the equation of a sphere in general form that is tangent to the plane defined by the equation x - 3y + 4z + 23 = 0 at the point (1, 4, -3) with a radius of √26. Participants suggest using the normal vector to the plane to determine the center of the sphere, which is crucial for establishing the sphere's equation. The normal vector can be derived from the coefficients of the plane equation, leading to two potential centers for the sphere based on the radius provided.
PREREQUISITESStudents studying geometry, particularly in three-dimensional space, as well as educators and tutors assisting with problems involving spheres and planes in mathematics.
Can you find a normal to the plane? It will point toward the center of the sphere (there will be two of them, though). And you know the radius of the sphere, so you should be able to find the center of the sphere.lolphysics3 said:Homework Statement
tangent to x-3y+4z+23=0 at (1,4,-3) with radius sqrt(26)
Homework Equations
The Attempt at a Solution
well i initially thought it's possible to set up a system of equations but it didn't work out.