3.1.16 Curves of the 2nd order
Condition: Find the canonical form of the given quadratic form and construct on the plane \( O X Y \) a line defined by the given equation. \[ 5 x_{1}^{2}-6 x_{1} x_{2}+5 x_{2}^{2}=32 \]
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.