3.1.25 Curves of the 2 -nd Order
Condition: the line is set by the equation \ (\ rho = \ rho (\ varphi) \) in the polar coordinate system. Required: build a line on points starting from \ (\ varphi = 0 \) to \ (\ varphi = 2 \ pi \), giving values with a step \ (\ pi / 8 \); Find the equation of this line in the Descartas rectangular coordinate system, in which the beginning coincides with the pole, and the positive axle of the abscissa is 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.