Option 29 DHS 4.1
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DHS - 4.1
№1.29. 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 = 34; ε = 15/17; A typo, as it should be ε <1; b) k = √17 / 8; 2c = 18; c) Oy axis of symmetry; A (4; –10).
№2.29. Write the equation of a circle passing through the indicated points and having a center at A. Given: Left focus of the ellipse 13x2 + 49y2 = 837; A (1; 8).
№3.29. To make the equation of the line, each point M of which satisfies the given conditions. The sum of squares of distances from point M to points A (–1; 2) and B (3; –1) is 18.5.
№4.29. Build a curve defined in the polar coordinate system: ρ = 2 / (2 - cos φ).
No. 5.29. Build a curve defined by parametric equations (0 ≤ t ≤ 2π)
№1.29. 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 = 34; ε = 15/17; A typo, as it should be ε <1; b) k = √17 / 8; 2c = 18; c) Oy axis of symmetry; A (4; –10).
№2.29. Write the equation of a circle passing through the indicated points and having a center at A. Given: Left focus of the ellipse 13x2 + 49y2 = 837; A (1; 8).
№3.29. To make the equation of the line, each point M of which satisfies the given conditions. The sum of squares of distances from point M to points A (–1; 2) and B (3; –1) is 18.5.
№4.29. Build a curve defined in the polar coordinate system: ρ = 2 / (2 - cos φ).
No. 5.29. Build a curve defined by parametric equations (0 ≤ t ≤ 2π)
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