№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 = 7; F (13; 0); b) b = 4; F (–11; 0); c) D: x = 13.

No. 2 Write down the equation of a circle passing through the indicated points and having a center at point A. Given: The right vertex of the hyperbola
x2 - 25 y2 = 75; A (–5; –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 = 2 at a distance five times greater than from point A (4; –3).

№4 Construct a curve defined in the polar coordinate system: ρ = 3 · (1 + cos2φ).

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