DHS - 4.1
№1.17. Make the canonical equation: a) an ellipse; b) hyperbole; c) parabolas; BUT; B - points lying on the curve; F - focus;
and - the big (real) semi-axis; b- small (imaginary) semi-axis; ε - eccentricity; y = ± k x - equations of the asymptotes of hyperbola; D is the director of the curve; 2c is the focal length. Given: a) 2a = 22; ε = 10/11; b) k = √11 / 5; 2c = 12; c) axis of symmetry Ox and A (–7; 5).
№2.17. Write the equation of a circle passing through the indicated points and having a center at A. Given: Left focus of the ellipse 3x2 + 7y2 = 21; A (–1; –3).
№3.17. To make 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 (–3; 3) and B (4; 1) is 31.
№4.17. Build a curve defined in the polar coordinate system: ρ = 3 / (1 - cos 2φ).
№5.17. Build a curve defined by parametric equations (0 ≤ t ≤ 2π)