Answer to Question #45099 in Analytic Geometry for jasvinder

Question

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.