# Answer to Question #46073 in Analytic Geometry for jasvinder

Question #46073

Find the new equation of the conicoid 184x^2 - 236xy + 88xz + 169y^2 - 14yz + 88z^2 =324 when the coordinate system xyz is transformed into another coordinate system x'y'z' under the transformations given by the following table:

x y z

x' 2/3 -2/3 1/3

y' 1/3 2/3 2/3

z' -2/3 -1/3 2/3

What object does this new equation represents in the coordinates system x'y'z' ?

Does the old equation represent the same object in the coordinate system xyz ?

Justify your answer.

x y z

x' 2/3 -2/3 1/3

y' 1/3 2/3 2/3

z' -2/3 -1/3 2/3

What object does this new equation represents in the coordinates system x'y'z' ?

Does the old equation represent the same object in the coordinate system xyz ?

Justify your answer.

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