IDZ Ryabushko 4.1 Variant 17
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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 = 22; ε = 10/11; b) k = √11 / 5; 2c = 12; c) axis of symmetry Ox and A (–7; 5).
№2 Write down the equation of a circle passing through the indicated points and having a center at point A. Given: Left focus of the ellipse 3x2 + 7y2 = 21; A (–1; –3).
№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 (–3; 3) and B (4; 1) is 31.
№4 Construct a curve defined in the polar coordinate system: ρ = 3 / (1 - cos 2φ).
№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 = 22; ε = 10/11; b) k = √11 / 5; 2c = 12; c) axis of symmetry Ox and A (–7; 5).
№2 Write down the equation of a circle passing through the indicated points and having a center at point A. Given: Left focus of the ellipse 3x2 + 7y2 = 21; A (–1; –3).
№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 (–3; 3) and B (4; 1) is 31.
№4 Construct a curve defined in the polar coordinate system: ρ = 3 / (1 - cos 2φ).
№5 Construct a curve given by parametric equations (0 ≤ t ≤ 2π)
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