3.1.25 Curves of the 2nd order
Condition: The line is given by the equation \( \rho=\rho(\varphi) \) in the polar coordinate system. Required: construct a line using points starting from \( \varphi=0 \) to \( \varphi=2 \pi \), giving values in increments \( \pi / 8 \); find the equation of this line in a Cartesian rectangular coordinate system, in which the origin coincides with the pole, and the positive semi-abscissa axis coincides with the polar axis. \[ \rho=2 \cos \varphi+1 \]
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.