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## Homework Statement

Find the points on the sphere x

^{2}+ y

^{2}+ z

^{2}= 1 where the tangent plane is parallel to the plane 2x + y - 3z = 2.

## Homework Equations

z - z

_{0}= f

_{x}(x

_{0}, y

_{0})(x - x

_{0}) + f

_{y}(x

_{0}, y

_{0})(y - y

_{0)})

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 x

_{0}and y

_{0}explicitly.

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