# Equation for a tilted parabola in 3D?

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