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Finding points on a sphere given a tangent plane that is parallel to a given plane

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Homework Statement



Find the points on the sphere x2 + y2 + z2 = 1 where the tangent plane is parallel to the plane 2x + y - 3z = 2.

Homework Equations



z - z0 = fx(x0, y0)(x - x0) + fy(x0, y0)(y - y0))

That's all I believe

The Attempt at a Solution



This chapter in our text does not require the use of vectors (eg dot and cross product), so I need to do this strictly algebraically. I found both first order partials, but didn't really know what to do after that. I plug in these partials to the expression above, but I don't think it's possible to solve for x0 and y0 explicitly.

If someone could guide me in the right direction, it would be much appreciated. Thank you all in advance!
 

Answers and Replies

  • #2
lanedance
Homework Helper
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first find the normal to the plane

then note any vector from the origin through, will be orthogonal to the sphere face where it intersects it
 

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