Equation of Sphere Homework: Center, Intersection & Equation

[joemama69]

Homework Statement

this problem has 3 parts

a- Determine an equation of the spere tha passes throught th epint 6,-2,3 and has center -1,2,1
b- Determine the curve in which this sphere intersects the yz plane
c- Determine the center and radius of the sphere x^2 + y^2 + z^2 - 8x + 2y + 6z + 1 = 0

Homework Equations

The Attempt at a Solution

a - r^2 = (6+1)^2 + (-2-2)^2 + (3-1)^2 = 69
(x+1)^2 + (y-2)^2 + (z-1)^2 = 69 is this corect

b - i don't really understand what the question is asking

c - center is (4,-1,-3)
r = (-1 + (8^2 + 2^2 + 6^2)/4)^1/2 = 5 is this correct

 

[Mark44]

a -- looks good
c -- looks good

For b, the y-z plane is the plane x = 0. You have the equation of the sphere, so just set x = 0 in that equation.

 

[joemama69]

sooooo...

1 + (y-2)² + (z-1)² = 69

 

[Mark44]

Works for me.