# Option 7 DHS 4.1 Collection of DHS Ryabushko

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## Description

DHS - 4.1
№1.7. 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 = 4; F (3; 0); b) b = 2√10; F (–11; 0); c) D: x = –2.
№2.7. Write the equation of a circle passing through the indicated points and having a center at point A. Given: Foci of the ellipse 3x2 + 4y2 = 12; A is its top peak.
No. 3.7. To make the equation of the line, each point M of which satisfies the given conditions. Distance from point A (4; 1) at a distance of four times more than from point B (–2; –1).
№4.7. Build a curve defined in the polar coordinate system: ρ = 2 · (1 - cosφ).
No. 5.7. Build a curve defined by parametric equations (0 ≤ t ≤ 2π)

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