3.1.37 Curves of the 2nd order
Condition: Determine the type of curve \[ 2 x^{2}+4 x y-4 y^{2}-4 x+4 y=4 \]
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.