Option 20 DHS 4.1

DHS - 4.1
№1.20. 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) b = 5; F (–10; 0); b) a = 9; ε = 4/3; c) D: x = 12.
№2.20. Write the equation of a circle passing through the indicated points and having a center at A. Given: The right vertex of the 3x2 hyperbola is 16y2 = 48; A (1 3).
№3.20. To make the equation of the line, each point M of which satisfies the given conditions. It is separated from the straight line x = –7 at a distance three times smaller than from point A (1; 4).
No. 4.20. Build a curve defined in the polar coordinate system: ρ = 5 · (2 ​​- sin φ).
No. 5.20. Build a curve defined by parametric equations (0 ≤ t ≤ 2π)