# Option 9 DHS 4.1 Collection of DHS Ryabushko

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## Description

DHS - 4.1
№1.9. 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 (0; √3); B (√14 / 3; 1); b) k = √21 / 10; ε = 11/10; c) D: y = - 4.
No. 2.9. Write the equation of a circle passing through the indicated points and having a center at A. Given: the foci of the hyperbola are 4x2– 5y2 = 80; A (0; –4).
No. 3.9. To make the equation of the line, each point M of which satisfies the given conditions. It is separated from the line y = 7 at a distance five times larger than from point A (4; –3).
№4.9. Build a curve defined in the polar coordinate system: ρ = 4 · sin 3φ.
No. 5.9. Build a curve defined by parametric equations (0 ≤ t ≤ 2π)

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