Option 1 DHS 4.1
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DHS - 4.1
№1.1. 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 = 15; F (–10; 0); b) a = 13; ε = 14/13; c) D: x = - 4.
№ 2.1. Write the equation of a circle passing through the indicated points and having a center at point A. Given: A (0; –2); vertices of the hyperbola 12x2 - 13y2 = 156.
No.3.1. Make an equation of the line, each point M of which satisfies the given conditions. It is separated from the line x = –6 at a distance twice as large; than from point A (1; 3).
No. 4.1. Build a curve defined in the polar coordinate system: ρ = 2 · sin 4φ.
# 5.1. Build a curve defined by parametric equations (0 ≤ t ≤ 2π)
№1.1. 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 = 15; F (–10; 0); b) a = 13; ε = 14/13; c) D: x = - 4.
№ 2.1. Write the equation of a circle passing through the indicated points and having a center at point A. Given: A (0; –2); vertices of the hyperbola 12x2 - 13y2 = 156.
No.3.1. Make an equation of the line, each point M of which satisfies the given conditions. It is separated from the line x = –6 at a distance twice as large; than from point A (1; 3).
No. 4.1. Build a curve defined in the polar coordinate system: ρ = 2 · sin 4φ.
# 5.1. Build a curve defined by parametric equations (0 ≤ t ≤ 2π)
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