Option 25 DHS 4.1 Collection of DHS Ryabushko

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Option 25 DHS 4.1 Collection of DHS Ryabushko

DHS - 4.1
№1.25. 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 = 13; F (–5; 0); b) b = 4; F (–7; 0); c) D: x = - 3/8.
№2.25. Write the equation of the circle; passing through the specified points and having a center at point A. The foci of the ellipse x2 + 10y2 = 90; A is its lower vertex.
№3.25. To make the equation of the line, each point M of which satisfies the given conditions. Distance from point A (5; 7) at a distance four times greater than from point B (–2; 1).
№4.25. Build a curve defined in the polar coordinate system: ρ = 4 · (1 - sin φ).
№5.25. Build a curve defined by parametric equations (0 ≤ t ≤ 2π)

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