№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 (0; –2); B (√15 / 2; 1); b) k = 2√20 / 9; ε = 11/9; c) y = 5.

№2 Write down the equation of a circle passing through the indicated points and having a center at point A. Given: Left focus of the hyperbola 7x2 - 9y2 = 63; A (–1; –2).

№3 Draw up the equation of the line, each point M of which satisfies the given conditions. It is spaced from the line x = 14 at a distance two times smaller than from point A (2; 3).

№4 Construct a curve defined in the polar coordinate system: ρ = 3 · sin 4φ.

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