№1 Make a canonical equation: a) an ellipse; b) hyperbole; c) parabolas; A; In - points lying on the curve; F is the focus; a - major (actual) axis; b - small (imaginary) axis; ε is the eccentricity; y = ± k x are the equations of the asymptotes of the hyperbola; D is the director of the curve; 2c is the focal length. Given: a) b = 2√2; ε = 7/9; b) k = √2 / 2; 2a = 12; c) The axis of symmetry of Oy and A (–45; 15).

№ 2 Write down the equation of a circle passing through the indicated points and having a center at point A. Given: Right focus of the hyperbola 57x2 - 64y2 = 3648; A (2; 8).

№3 Draw up the equation of the line, each point M of which satisfies the given conditions. It is separated from point A (1; 5) by a distance three to four times smaller than from the line x = - 1.

№4 Construct a curve defined in the polar coordinate system: ρ = 2 - cos 2φ.

№5 Construct a curve given by parametric equations (0 ≤ t ≤ 2π)