Option 16 DHS 4.1

DHS - 4.1
№1.16. 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) ε = 3/5; A (0; 8); b) A (√6; 0); B (-2√2; 1); c) D: y = 9.
No. 2.16. Write down the equation of a circle passing through the indicated points and having a center at point A. Given: B (1; 4); A is the vertex of the parabola y2 = (x - 4) / 3.
No. 3.16. Make an equation of the line, each point M of which satisfies the given conditions. The ratio of the distances from point M to points A (2; –4) and B (3; 5) is 2/3.
№4.16. Build a curve defined in the polar coordinate system: ρ = 2 · cos 6φ.
№5.16. Build a curve defined by parametric equations (0 ≤ t ≤ 2π)