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 z = x^2 + y^2 where ( x , y , z ) = ( 0 , 0 , 0 ) (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 z = x^2 + y^2 at the point ( x , y , z ) = ( 1 , 2 , 5 ) (x,y,z) = (1,2,5) ?

2x + 4y - z - 5 = 0 x + 2y + z - 10 = 0 2x + 2y - z = 0 2x + 4y + z - 15 = 0

Guillermo Templado by Guillermo Templado , 46, Spain

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