IDZ Ryabushko 4.1 Variant 13

№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 = 6; F (–4; 0); b) b = 3; F (7; 0); c) D: x = - 7.

№2 Write down the equation of a circle passing through the indicated points and having a center at point A. Foci of the ellipse 16x2 + 41y2 = 656; A is its lower peak.

№3 Draw up the equation of the line, each point M of which satisfies the given conditions. It is three times more from point A (–3; 3) than from point B (5; 1).

№4 Construct a curve defined in the polar coordinate system: ρ = 5 · (1 - sin 2φ).

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