Option 5 DHS 4.1 Collection of DHS Ryabushko

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Option 5 DHS 4.1 Collection of DHS Ryabushko

DHS - 4.1
№1.5. 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 the hyperbola; D is the director of the curve; 2c is the focal length. Given: a) 2a = 22; ε = √57 / 11; b) k = 2/3; 2c = 10√13; c) axis of symmetry Ox and A (27; 9).
No. 2.5. Write the equation of the circle; passing through the specified points and having a center at point A. The foci of the ellipse 9x2 + 25y2 = 1; A 0; 6).
№3.5. Make an 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 (4; 0) and B (–2; 2) is 28.
№4.5. Build a curve defined in the polar coordinate system: ρ = 2 / (1 + cosφ).
No. 5.5. Build a curve defined by parametric equations (0 ≤ t ≤ 2π)


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