Find the equation of the sphere that passes through the point (6,-2,3) and has centre (-1,2,1).
(b) find the curve in which this sphere intersects the yz-plane
(c) find the center and radius of the sphere
x^2 + y^2 + z^2 - 8x + 2y+ 6z+1=0

a) The sphere has radius equal to the distance between the center and the given point:

So the sphere has equation

b) The sphere intersects the - plane whenever :

which is the equation of the circle centered at (-2, 3) with radius .

c) Complete the squares:

So this sphere has radius 5 and is centered at (4, -1, -3).

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step-by-step explanation:

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