№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 = √15; ε = √10 / 25; b) k = 3/4; 2a = 16; c) axis of symmetry Ox; A (4; –8).

№2 Write down the equation of a circle passing through the indicated points and having the center at point A. Given: Left focus of the hyperbola 3x2– 4y2 = 12; A (0; –3).
№3 Draw up the equation of the line, each point M of which satisfies the given conditions. It is distant from point A (1; 0) at a distance five times smaller than from straight line x = 8.

№4 Construct a curve defined in the polar coordinate system: ρ = 3 · (1 + sin φ)

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