№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; F (4√2; 0); b) a = 7; ε = √85 / 7; c) D: x = 5.

№2 Write down the equation of a circle passing through the indicated points and having a center at point A. Given: the vertices of the hyperbola 4x2 - 9y2 = 36; A (0; 4).

№3 Draw up the equation of the line, each point M of which satisfies the given conditions. It is spaced from the line x = –2 at a distance twice as large; than from point A (4; 0).

№4 Construct a curve defined in the polar coordinate system: ρ = 2 · (1 - sin 2φ).

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