IDZ Ryabushko 4.1 Variant 11
Content: 4.1 - 11.pdf (88.49 KB)
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№1 Make a canonical equation: a) an ellipse; b) hyperbole; c) parabolas; A; In - points lying on the curve; F is the focus;
a - major (actual) axis; b - small (imaginary) axis; ε is the eccentricity; y = ± k x are the equations of the asymptotes of the hyperbola; D is the director of the curve; 2c is the focal length. Given: a) 2a = 24; ε = √22 / 6; b) k = √2 / 3; 2c = 10; c) axis of symmetry Ox and A (–7; –7).
№2 Write down the equation of a circle passing through the indicated points and having a center at point A. Given: Right focus of the ellipse 33x2 + 49y2 = 1617; A (1; 7).
№3 Draw up the equation of the line, each point M of which satisfies the given conditions. The sum of the squares of the distances from point M to points A (–5; –1) and B (3; 2) is 40.5.
№4 Construct a curve defined in the polar coordinate system: ρ = 3 · (1 + cos φ).
№5 Construct a curve given by parametric equations (0 ≤ t ≤ 2π)
a - major (actual) axis; b - small (imaginary) axis; ε is the eccentricity; y = ± k x are the equations of the asymptotes of the hyperbola; D is the director of the curve; 2c is the focal length. Given: a) 2a = 24; ε = √22 / 6; b) k = √2 / 3; 2c = 10; c) axis of symmetry Ox and A (–7; –7).
№2 Write down the equation of a circle passing through the indicated points and having a center at point A. Given: Right focus of the ellipse 33x2 + 49y2 = 1617; A (1; 7).
№3 Draw up the equation of the line, each point M of which satisfies the given conditions. The sum of the squares of the distances from point M to points A (–5; –1) and B (3; 2) is 40.5.
№4 Construct a curve defined in the polar coordinate system: ρ = 3 · (1 + cos φ).
№5 Construct a curve given by parametric equations (0 ≤ t ≤ 2π)
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