Option 8 DHS 4.1

Option 8 DHS 4.1

DHS - 4.1
№1.8. 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 = 4; F (9; 0); b) a = 5; ε = 7/5; c) D: x = 6.
№2.8. Write the equation of a circle passing through the vertex of the hyperbola x2 - 16y2 = 64 and having a center at the point A (0; –2).
# 3.8. Make an equation of the line, each point M of which satisfies the given conditions. Is separated from the line x = - 5 at a distance of three times as large; than from point A (6; 1).
№4.8. Build a curve defined in the polar coordinate system: ρ = 3 · (1 - cos2φ).
No. 5.8. Build a curve defined by parametric equations (0 ≤ t ≤ 2π)