Option 23 DHS 4.1 Collection of DHS Ryabushko

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DHS - 4.1
№1.23. 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) 2a = 50; ε = 3/5; b) k = √29 / 14; 2c = 30; c) the axis of symmetry of Oy and A (4; 1).
№2.23. Write the equation of a circle passing through the indicated points and having a center at A. Given: The right focus of the ellipse x2 + 4y2 = 12; A (2; –7).
№3.23. To make the equation of the line, each point M of which satisfies the given conditions. The sum of the squares of the distances from point M to points A (–5; 3) and B (2; –4) is 65.
№4.23. Build a curve defined in the polar coordinate system: ρ = 4 · (1 + cos 2φ).
№5.22. Build a curve defined by parametric equations (0 ≤ t ≤ 2π)

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