3.1.19 Curves of the 2nd order
condition: Having performed sequential coordinate transformations: rotation and then parallel translation of coordinate axes, transform the equation of the second-order curve to canonical form and construct it in the original coordinate system, as well as find the parameters of the curve. \[ 5 x^{2}+4 x y+8 y^{2}-36=0 \]
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.