Option 10 DHS 4.1 Collection of DHS Ryabushko

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Option 10 DHS 4.1 Collection of DHS Ryabushko

DHS - 4.1
№1.10. 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) ε = 7/8; A (8; 0); b) A (3; -√3 / 5); B (√13 / 5; 6); c) D: y = 4. point b) is not a valid condition
No. 2.10. Write the equation of a circle passing through the specified points and having a center at point A. Given: O (0; 0); A is the vertex of the parabola y2 = - (x + 5) / 2.
№ 3.10. Make an equation of the line, each point M of which satisfies the given conditions. The ratio of the distances from point M to points A (–3; 5) and B (4; 2) is 1/3.
№ 4.10. Build a curve defined in the polar coordinate system: ρ = 4 · sin 4φ.
№ 5.10. Build a curve defined by parametric equations (0 ≤ t ≤ 2π)

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