Option 6 DHS 4.1

DHS - 4.1
№1.6. 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) b = √15; ε = √10 / 25; b) k = 3/4; 2a = 16; c) axis of symmetry Ox; A (4; –8).
№2.6. Write the equation of a circle passing through the indicated points and having a center at the point A. Given: Left focus of the hyperbola 3x2– 4y2 = 12; A (0; –3).
No. 3.6. Make an equation of the line, each point M of which satisfies the given conditions. It is separated from point A (1; 0) at a distance five times smaller than from the line x = 8.
№4.6. Build a curve defined in the polar coordinate system: ρ = 3 · (1 + sin φ)
No. 5.6. Build a curve defined by parametric equations (0 ≤ t ≤ 2π)