In the discriminant test of conic sections(rotations), why we're checking with $B^2-4AC$. How $B^2-4AC=B'^2-4A'C'$, where $Ax^2+Bxy+Cy^2+Dx+Ey+F=0$ is changed to $A'x^2+C'y^2+D'x+E'y+F'=0$ using rotations by angle alpha.
rotation of conic sections
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conic-sections
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0You need to do the replacements of $x,y$ by the rotation, and then find the new $A',B'$ etc, and just compute $B'^2-A'C'$. If you have rotated so as to eliminate the $xy$ term, the $B'$ will be zero here. – 2012-10-22