3.1.14 Curves of the 2nd order
Condition: Determine the type of curve, bring the equation to canonical form: \( 2 x^{2}+2 x y-2 y^{2}-4 x+2 y=2 \).
Study of curves of the second order and their characteristics. Ellipse, hyperbola, parabola. Finding eccentricities, foci, focal radii, major and minor axes, including imaginary, canonical equations and plotting.