№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 = 5; ε = 12/13; b) k = 1/3; 2a = 6; c) The axis of symmetry of Oy and A (–9; 6).
№2 Write down the equation of a circle passing through the indicated points and having a center at point A. The left vertex of the hyperbola is 5x2 - 9y2 = 45; A (0; –6).
№3 Draw up the equation of the line, each point M of which satisfies the given conditions. It is located at a distance from the point A (0; –5), two times less than to the line x = 3.
№4 Construct a curve defined in the polar coordinate system: ρ = 2 · (1 - cos3φ).
№5 Construct a curve given by parametric equations (0 ≤ t ≤ 2π)
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