3.1.26 Curves of the 2nd order
Condition: Bring the equation of the second order curve to canonical form. Make a drawing. \[ 13 x^{2}+32 x y+37 y^{2}+46 x+22 y+13=0 . \]
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.