3.1.44 Curves of the 2nd order
condition: Find the canonical equation and determine the type of the second-order line: \[ 5 x^{2}+12 x y-22 x-12 y-19=0 \]
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.