Option 15 DHS 4.1

DHS - 4.1
№1.15. 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) A (-√17 / 3; 1/3); B (√21 / 2; 1/2); b) k = 1/2; ε = √5 / 2; c) D: y = - 1.
No. 2.15. Write the equation of a circle passing through the indicated points and having a center at A. Given: Focus points of the 5x2 hyperbola - 11y2 = 55; A (0; 5).
№3.15. Make an equation of the line, each point M of which satisfies the given conditions. It is separated from the line x = 9 at a distance four times smaller than from point A (–1; 2).
№4.15. Build a curve defined in the polar coordinate system: ρ = 6 · sin 4φ.
No. 5.15. Build a curve defined by parametric equations (0 ≤ t ≤ 2π)