# Option 30 DHS 4.1 Collection of DHS Ryabushko

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## Description

DHS - 4.1
№1.30. 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) b = 2√2; ε = 7/9; b) k = √2 / 2; 2a = 12; c) Oy and A axis of symmetry (–45; 15).
No. 2.30. Write the equation of a circle passing through the indicated points and having a center at A. Given: The right focus of the hyperbola is 57x2 - 64y2 = 3648; A (2; 8).
№ 3.30. To make the equation of the line, each point M of which satisfies the given conditions. It is separated from point A (1; 5) at a distance of three to four times less than from the line x = - 1.
№ 4.30. Build a curve defined in the polar coordinate system: ρ = 2 - cos 2φ.
No. 5.30. Build a curve defined by parametric equations (0 ≤ t ≤ 2π)

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