DHS - 4.1
№1.14. 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) b = 7; F (5; 0); b) a = 11; ε = 12/11; c) D: x = 10.
No. 2.14. Write the equation of a circle passing through the indicated points and having a center at A. Dano: The vertex of the hyperbola is 2x2–9y2 = 18; A (0; 4).
No. 3.14. Make an equation of the line, each point M of which satisfies the given conditions. It is separated from the line x = 8 at a distance twice as large as from point A (–1; 7).
№4.14. Build a curve defined in the polar coordinate system: ρ = 3 · (2 ​​- cos 2φ).
№5.14. Build a curve defined by parametric equations (0 ≤ t ≤ 2π)