IDZ Ryabushko 4.1 Variant 12
Content: 4.1 - 12.pdf (92.40 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) b = 2; ε = 5√29 / 29; b) k = 12/13; 2a = 26; c) axis of symmetry Ox and A (–5; 15).
№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 hyperbola 3x2–5y2 = 30; A (0; 6).
№3 Draw up the equation of the line, each point M of which satisfies the given conditions. It is three times larger from point A (2; 1) than from line x = –5.
№4 Construct a curve defined in the polar coordinate system: ρ = 1 / (2-sin 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) b = 2; ε = 5√29 / 29; b) k = 12/13; 2a = 26; c) axis of symmetry Ox and A (–5; 15).
№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 hyperbola 3x2–5y2 = 30; A (0; 6).
№3 Draw up the equation of the line, each point M of which satisfies the given conditions. It is three times larger from point A (2; 1) than from line x = –5.
№4 Construct a curve defined in the polar coordinate system: ρ = 1 / (2-sin φ).
№5 Construct a curve given by parametric equations (0 ≤ t ≤ 2π)
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