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Exercises

For each of the following 2nd order curbes write its canonical form and sketch it in the original (x,y)-coordinates.

$5x^2 + 4 x \cdot y + 8 y^2 + x + 2y =0$

$-x^2 + 2\sqrt{2} x\cdot y + x + 1 = 0$

$x^2 + 4\cdot xy + 4 y^2 + x + y + 2 =0$

$x^2 + 8x\cdot y + y^2 +x - y - 2 =0$

$5x^2 + 8 x \cdot y + 5 y^2 - 2y + 1 = 0$

$-x^2 + 4\sqrt{3} xy - 2x + 1 =0$