# Option 3 DHS 4.1 Collection of DHS Ryabushko

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## Description

DHS - 4.1
№ 1.3. 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 (2; √5 / 3); b) k = 3/4; ε = 5/4; c) D: y = - 2.
№2.3. Write the equation of a circle passing through the indicated points and having a center at the point A. Given: Foci of the hyperbola 24y2 - 25x2 = 600; A (–8; 0).
№3.3. Make an equation of the line, each point M of which satisfies the given conditions. It is separated from the line y = –2 at a distance of three times as large; than from point A (5; 0).
№4.3. Build a curve defined in the polar coordinate system: ρ = 2 · sin 2φ.
No. 5.3. Build a curve defined by parametric equations (0 ≤ t ≤ 2π)

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