Option 22 DHS 4.1
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DHS - 4.1
№1.22. 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 = 2/3; A (–6; 0; b) A (√8; 0); c) D: y = 1.
b) Not the right condition. The coordinates of the points are wrong. Not solved
№2.22. Write down the equation of a circle passing through the indicated points and having a center at point A. Given: B (2; –5); A is the vertex of the parabola x2 = –2 · (y +1).
№3.22. Make an equation of a line, each point M of which satisfies the conditions: The ratio of the distances from point M to points A (3; –2) and B (4; 6) is 3/5.
№4.22. Build a curve defined in the polar coordinate system: ρ = 2 · cos 4φ.
№5.22. Build a curve defined by parametric equations (0 ≤ t ≤ 2π)
№1.22. 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 = 2/3; A (–6; 0; b) A (√8; 0); c) D: y = 1.
b) Not the right condition. The coordinates of the points are wrong. Not solved
№2.22. Write down the equation of a circle passing through the indicated points and having a center at point A. Given: B (2; –5); A is the vertex of the parabola x2 = –2 · (y +1).
№3.22. Make an equation of a line, each point M of which satisfies the conditions: The ratio of the distances from point M to points A (3; –2) and B (4; 6) is 3/5.
№4.22. Build a curve defined in the polar coordinate system: ρ = 2 · cos 4φ.
№5.22. Build a curve defined by parametric equations (0 ≤ t ≤ 2π)
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