IDZ Ryabushko 4.1 Variant 16
Content: 4.1 - 16.pdf (109.86 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) ε = 3/5; A (0; 8); b) A (√6; 0); B (-2√2; 1); c) D: y = 9.
№2 Write down the equation of a circle passing through the indicated points and having a center at point A. Given: B (1; 4); A is the vertex of the parabola y2 = (x - 4) / 3.
№3 Draw up the equation of the line, each point M of which satisfies the given conditions. The ratio of the distances from point M to points A (2; –4) and B (3; 5) is 2/3.
№4 Construct a curve defined in the polar coordinate system: ρ = 2 · cos 6φ.
№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) ε = 3/5; A (0; 8); b) A (√6; 0); B (-2√2; 1); c) D: y = 9.
№2 Write down the equation of a circle passing through the indicated points and having a center at point A. Given: B (1; 4); A is the vertex of the parabola y2 = (x - 4) / 3.
№3 Draw up the equation of the line, each point M of which satisfies the given conditions. The ratio of the distances from point M to points A (2; –4) and B (3; 5) is 2/3.
№4 Construct a curve defined in the polar coordinate system: ρ = 2 · cos 6φ.
№5 Construct a curve given by parametric equations (0 ≤ t ≤ 2π)
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