Equation for a tilted parabola in 3D?

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  • #1
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So I was doodling around and came up with a problem of finding an equation for a tilted parabola. Basically, a parabola in xy plane which was rotated around a line that goes through points (1,0) and (0,1), making the curve a 3D one. I realize that this curve is a subset of points that define a paraboloid but I have no clue how to extract one from the other. Any help? Here's a picture for visual guidance http://i.imgur.com/6Esnhkh.png
 

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  • #2
HallsofIvy
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When you say "a parabola in the xy-plane" which parabola do you mean? If you rotate a parabola around any other line but its axis, the result is NOT a paraboloid.
 
  • #3
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When you say "a parabola in the xy-plane" which parabola do you mean? If you rotate a parabola around any other line but its axis, the result is NOT a paraboloid.
Sorry for being unclear. I do not mean a solid of revolution. I mean taking a parabola which lies on the xy plane and rotating it (moving all of its points) by some amount of degrees around an axis (in my case a line which goes through points (1,0) and (0,1). If you look at the picture it represents a rotated parabola which "had" its points of intersection with x and y axes fixed.
 

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