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

## 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!

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lanedance
Homework Helper

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