How can you tell which axis the graph is oriented on? Obviously this is very easy for a hyperbolic paraboloid, but what about for the equation x^2+y^2-z^2=0?

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- Jan 25th 2006, 09:52 AMAK713[SOLVED] quadric surfaces
How can you tell which axis the graph is oriented on? Obviously this is very easy for a hyperbolic paraboloid, but what about for the equation x^2+y^2-z^2=0?

- Jan 25th 2006, 10:57 AMticbolQuote:

Originally Posted by**AK713**

Rearranging that,

x^2 +y^2 = z^2 ----------(ii)

The LHS of (ii) is a circle.

The RHS is a square of a z-coordinate. It could be the square of the radius of the LHS at the z-coordinate.

When z=0, the circle at the LHS is zero too, or no circle. It is (0,0,0), or the origin.

When z = 1, or z = -1, the circle at the LHS has a radius of 1.

When z = 2, or z = -2, the circle at the LHS has a radius of 2.

When z = 3, or z = -3, the circle at the LHS has a radius of 3.

Etc...

The figure then is that of a cone whose apex is at the (0,0,0) and opening upwards, and that of its mirror-shape that opens downward.

That is if the z-axis is the usual up-down or vertical axis in the x,y,z axes setup.