- #1
BrainHurts
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If the hyperbolic paraboloid z=(x/a)^2 - (y/b)^2
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?
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?