Find the points on the surface at which the tangent plane is parallel to the plane .
How do I get started?
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Originally Posted by zpwnchen How do I get started?
Find the points on the surface at which the tangent plane is parallel to the plane . Parallel planes have the same normal vector (i.e. ). The constant term is irrelevant.
The equation for the tangent plane is
So you want , , and (because you have to take into account the normal vector can be scaled by any constant ). Spoiler: So the points are .
Now you need to solve for given the initial equation:
So the two points are: and
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