Option 18 DHS 4.1
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DHS - 4.1
№1.18. 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 hyperbola; D is the director of the curve; 2c is the focal length. Given: a) b = 5; ε = 12/13; b) k = 1/3; 2a = 6; c) Oy and A axis of symmetry (–9; 6).
№ 2.18. Write the equation of a circle passing through the specified points and having a center at A. The left vertex of the hyperbola is 5x2 - 9y2 = 45; A (0; –6).
No. 3.18. To make the equation of the line, each point M of which satisfies the given conditions. It is separated from the point A (0; –5) at a distance that is two times smaller than the straight line x = 3.
No. 4.18. Build a curve defined in the polar coordinate system: ρ = 2 · (1 - cos3φ).
No. 5.18. Build a curve defined by parametric equations (0 ≤ t ≤ 2π)
№1.18. 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 hyperbola; D is the director of the curve; 2c is the focal length. Given: a) b = 5; ε = 12/13; b) k = 1/3; 2a = 6; c) Oy and A axis of symmetry (–9; 6).
№ 2.18. Write the equation of a circle passing through the specified points and having a center at A. The left vertex of the hyperbola is 5x2 - 9y2 = 45; A (0; –6).
No. 3.18. To make the equation of the line, each point M of which satisfies the given conditions. It is separated from the point A (0; –5) at a distance that is two times smaller than the straight line x = 3.
No. 4.18. Build a curve defined in the polar coordinate system: ρ = 2 · (1 - cos3φ).
No. 5.18. Build a curve defined by parametric equations (0 ≤ t ≤ 2π)
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