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Elliptic Paraboloid
The equation which is given here is the equation of an elliptic paraboloid.
x2/a2 + y2/b2 = z/c
Like with cylinders this has a cross section of an ellipse and if a = b it will comprise a cross section of a circle. While we deal with these we'll usually be dealing with the type that has a circle for a cross section.
Here is a diagram of a typical elliptic paraboloid.
In this type of case the variable that isn't squared find outs the axis upon which the paraboloid opens up. As well, the sign of c will determine the direction that the paraboloid opens. If c is positive after that it opens up and if c is negative then it opens down.
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solve: 4ydx+xdy=0
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