Option 19 DHS 4.1

DHS - 4.1
№1.19. 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 = 9; F (7; 0); b) b = 6; F (2; 0); c) D: x = - 1/4.
№2.19. Write the equation of a circle passing through the specified points and having a center at A. Foci of the ellipse 24x2 + 25y2 = 600; A is its top vertex.
№3.19. To make the equation of the line, each point M of which satisfies the given conditions. It is separated from point A (4; –2) at a distance two times smaller than from point B (1; 6).
№4.19. Build a curve defined in the polar coordinate system: ρ = 3 · (1 - cos4φ).
№5.19. Build a curve defined by parametric equations (0 ≤ t ≤ 2π)