Option 12 DHS 4.1
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DHS - 4.1
№1.12. 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 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).
№2.12. Write the equation of a circle passing through the indicated points and having a center at A. Given: Left focus of the hyperbola 3x2–5y2 = 30; A (0; 6).
№ 3.12. Make an equation of the line, each point M of which satisfies the given conditions. It is separated from point A (2; 1) at a distance three times longer than from the straight line x = –5.
№ 4.12. Build a curve defined in the polar coordinate system: ρ = 1 / (2-sin φ).
№ 5.12. Build a curve defined by parametric equations (0 ≤ t ≤ 2π)
№1.12. 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 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).
№2.12. Write the equation of a circle passing through the indicated points and having a center at A. Given: Left focus of the hyperbola 3x2–5y2 = 30; A (0; 6).
№ 3.12. Make an equation of the line, each point M of which satisfies the given conditions. It is separated from point A (2; 1) at a distance three times longer than from the straight line x = –5.
№ 4.12. Build a curve defined in the polar coordinate system: ρ = 1 / (2-sin φ).
№ 5.12. Build a curve defined by parametric equations (0 ≤ t ≤ 2π)
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