№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) 2a = 22; ε = √57 / 11; b) k = 2/3; 2c = 10√13; c) axis of symmetry Ox and A (27; 9).

No. 2 Write the equation of a circle; passing through the indicated points and having a center at point A. Foci of the ellipse 9x2 + 25y2 = 1; A 0; 6).

№3 Draw up the equation of the line, each point M of which satisfies the given conditions. The sum of the squares of the distances from point M to points A (4; 0) and B (–2; 2) is 28.

№4 Construct a curve defined in the polar coordinate system: ρ = 2 / (1 + cosφ).

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