3.1.17 Curves of the 2nd order
condition: Using parallel translation and rotation of the coordinate system, bring the equation of the line to canonical form and construct a graph of this line. \[ 7 x^{2}+6 x y-y^{2}+28 x+12 y+28=0 \]
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.