Shape of Universe?

Geometry Level 3

Suppose that the universe had a beginning in the Big Bang, and currently is expanding. For example, suppose that the universe is in the form of an elliptical paraboloid \(z = x^2 + y^2\) where \((x,y,z) = (0,0,0)\) represents the Big Bang... The question is:

What is the plane tangent to the elliptic paraboloid \(z = x^2 + y^2\) at the point \((x,y,z) = (1,2,5)\)?

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