91Ó°ÊÓ

Perform a rotation of axes to eliminate the \(x y\) -term, and sketch the graph of the "degenerate" conic. $$x^{2}-2 x y+y^{2}=0$$

Perform a rotation of axes to eliminate the \(x y\) -term, and sketch the graph of the "degenerate" conic. $$x^{2}-2 x y+5 y^{2}=0$$

Determine if the third column can be written as a linear combination of the first two columns. $$\left[\begin{array}{lll} 1 & 2 & 3 \\ 7 & 8 & 9 \\ 4 & 5 & 6 \end{array}\right]$$

Prove that a rotation of \(\theta,\) where cot \(2 \theta=(a-c) / b,\) will eliminate the \(x y\) -term from the equation $$a x^{2}+b x y+c y^{2}+d x+e y+f=0$$