№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) A (3; 0); B (2; √5 / 3); b) k = 3/4; ε = 5/4; c) D: y = - 2.

№2 Write down the equation of a circle passing through the indicated points and having a center at point A. Given: Foci of the hyperbola 24y2 - 25x2 = 600; A (–8; 0).

№3 Draw up the equation of the line, each point M of which satisfies the given conditions. It is spaced from the line y = –2 at a distance of three times greater; than from point A (5; 0).

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

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