Option 11 DHS 4.1

DHS - 4.1
№1.11. 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 the hyperbola; D is the director of the curve; 2c is the focal length. Given: a) 2a = 24; ε = √22 / 6; b) k = √2 / 3; 2c = 10; c) axis of symmetry Ox and A (–7; –7).
№2.11. Write the equation of a circle passing through the indicated points and having a center at A. Given: Right focus of the ellipse 33x2 + 49y2 = 1617; A (1; 7).
№ 3.11. Make an 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 (–5; –1) and B (3; 2) is 40.5.
№4.11. Build a curve defined in the polar coordinate system: ρ = 3 · (1 + cos φ).
№ 5.11. Build a curve defined by parametric equations (0 ≤ t ≤ 2π)