3.1.13 Curves of the 2nd order
Condition: Given the equation \[ 9 x^{2}+9 y^{2}-9 x-6 y-(23 / 4)=0 \] a) determine the type of curve; b) lead to canonical form; c) construct a curve.
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.