DHS - 4.1
№1.21. 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) A (0; –2); B (√15 / 2; 1); b) k = 2√20 / 9; ε = 11/9; c) y = 5.
№2.21. Write the equation of a circle passing through the indicated points and having a center at A. Given: Left focus of hyperbola 7x2 - 9y2 = 63; A (–1; –2).
№3.21. To make the equation of the line, each point M of which satisfies the given conditions. It is separated from the line x = 14 at a distance two times smaller than from point A (2; 3).
No. 4.21. Build a curve defined in the polar coordinate system: ρ = 3 · sin 4φ.
No. 5.21. Build a curve defined by parametric equations (0 ≤ t ≤ 2π)