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I have no idea what to do for this problem. Any help would be appreciated.

Consider the sphere S of radius 5 centred at (1, 0,2). Find the equation of the plane tangent to S at the point (5,-3,2).

Hint: To get started, draw this situation in 2D with a circle.

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Questioner:Nick
Country:Quebec, Canada
Category:Advanced Math
Private:No
Subject:Linear Algebra

Question:

I have no idea what to do for this problem. Any help would be appreciated.

Consider the sphere S of radius 5 centred at (1, 0,2). Find the equation of the plane tangent to S at the point (5,-3,2).

Hint: To get started, draw this situation in 2D with a circle.
..............................................


The vector form of the equation of a plane is:

normalvector dot (<x,y,z> - <x0,y0,z0>) = 0

since the normal vector is, er..  normal to any vector in the plane. (duh...)

So take your  <x0,y0,z0> to be (1,0,2), the point IN the plane, and
take the normal to be vector CP.  (C is the center, P is the point of tangency.)

That should do it.

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