# Option 27 DHS 4.1 Collection of DHS Ryabushko

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## Description

DHS - 4.1
No. 1.27. 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 (–3; 0); B (1; √40 / 3); b) k = √2 / 3; ε = √15 / 3; c) D: y = 4.
No. 2.27. Write the equation of a circle passing through the indicated points and having a center at the point A. Given: Focus points of the 4x2 hyperbola - 5y2 = 20; A (0; –6).
№ 3.27. To make the equation of the line, each point M of which satisfies the given conditions. It is separated from the straight line x = - 7 at a distance three times smaller than from point A (3; 1).
No. 4.27. Build a curve defined in the polar coordinate system: ρ = 3 · cos 2φ.
No. 5.27. Build a curve defined by parametric equations (0 ≤ t ≤ 2π)

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