Option 28 DHS 4.1
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DHS - 4.1
№ 1.28. 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 = 5/6; A (0; -√11); b) A (√32 / 3; 1); B (√8; 0); c) D: y = - 3.
No. 2.28. Write down the equation of a circle passing through the specified points and having a center at point A. Given: B (3; 4); A - the top of a parabola; y2 = (x + 7) / 4.
№ 3.28. To make the 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; 1) is 1/4.
No. 4.28. Build a curve defined in the polar coordinate system: ρ = 2 · sin 3φ.
No. 5.28. Build a curve defined by parametric equations (0 ≤ t ≤ 2π)
№ 1.28. 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 = 5/6; A (0; -√11); b) A (√32 / 3; 1); B (√8; 0); c) D: y = - 3.
No. 2.28. Write down the equation of a circle passing through the specified points and having a center at point A. Given: B (3; 4); A - the top of a parabola; y2 = (x + 7) / 4.
№ 3.28. To make the 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; 1) is 1/4.
No. 4.28. Build a curve defined in the polar coordinate system: ρ = 2 · sin 3φ.
No. 5.28. Build a curve defined by parametric equations (0 ≤ t ≤ 2π)
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