IDZ Ryabushko 4.1 Variant 29
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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 = 34; ε = 15/17; Typo, as it should be ε <1; b) k = √17 / 8; 2c = 18; c) Oy axis of symmetry; A (4; –10).
№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 13x2 + 49y2 = 837; A (1; 8).
№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 (–1; 2) and B (3; –1) is 18.5.
№4 Construct a curve defined in the polar coordinate system: ρ = 2 / (2 - cos φ).
№5 Construct a curve given by parametric equations (0 ≤ t ≤ 2π)
№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 13x2 + 49y2 = 837; A (1; 8).
№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 (–1; 2) and B (3; –1) is 18.5.
№4 Construct a curve defined in the polar coordinate system: ρ = 2 / (2 - cos φ).
№5 Construct a curve given by parametric equations (0 ≤ t ≤ 2π)
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