Option 4 DHS 4.1

Option 4 DHS 4.1

DHS - 4.1
№1.4. 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) ε = √21 / 5; A (–5; 0); b) A (√80; 3); B (4√6; 3√2); c) D: y = 1.
No. 2.4. Write the equation of a circle passing through the specified points and having a center at point A. Given: 0 (0; 0); A is the vertex of the parabola y2 = 3 (x - 4).
No. 3.4. 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; 3) and B (–1; 2) is equal to 3/4.
№4.4. Build a curve defined in the polar coordinate system: ρ = 3 · sin 6φ.
No. 5.4. Build a curve defined by parametric equations (0 ≤ t ≤ 2π)