If the hyperbolic paraboloid z=(x/a)^2 - (y/b)^2(adsbygoogle = window.adsbygoogle || []).push({});

is rotated by an angle of π/4 in the +z direction (according to the right hand rule), the result is the surface

z=(1/2)(x^2 + y^2) ((1/a^2)-((1/b^2)) + xy((1/a^2)-((1/b^2))

and if a= b then this simplifies to

z=2/(a^2) (xy)

suppose z= x^2 - y^2

does this mean that z=2xy ?

if so can someone tell me how to put z=x^2 - y^2 into it's quadric form? Also the rotation by the angle of π/4 is that just the typical rotation matrix Rz?

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# Hyperbolic Paraboloid and Isometry

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