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Option 13 DHS 4.1 Collection of DHS Ryabushko
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DHS - 4.1
№1.13. 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) a = 6; F (–4; 0); b) b = 3; F (7; 0); c) D: x = - 7.
№2.13. Write the equation of a circle passing through the indicated points and having a center at A. Foci of the ellipse 16x2 + 41y2 = 656; A is its lower vertex.
No. 3.13. To make the equation of the line, each point M of which satisfies the given conditions. It is separated from point A (–3; 3) at a distance of three times more than from point B (5; 1).
№4.13. Build a curve defined in the polar coordinate system: ρ = 5 · (1 - sin 2φ).
№5.13. Build a curve defined by parametric equations (0 ≤ t ≤ 2π)