IDZ Ryabushko 4.1 Variant 10
Content: 4.1 - 10.pdf (105.88 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 = 7/8; A (8; 0); b) A (3; -√3 / 5); B (√13 / 5; 6); c) D: y = 4. clause b) false condition
№2 Write down the equation of a circle passing through the indicated points and having a center at point A. Given: O (0; 0); A is the vertex of the parabola y2 = - (x + 5) / 2.
№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 (–3; 5) and B (4; 2) is 1/3.
№4 Construct a curve defined in the polar coordinate system: ρ = 4 · sin 4φ.
№5 Construct a curve given by parametric equations (0 ≤ t ≤ 2π)
№2 Write down the equation of a circle passing through the indicated points and having a center at point A. Given: O (0; 0); A is the vertex of the parabola y2 = - (x + 5) / 2.
№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 (–3; 5) and B (4; 2) is 1/3.
№4 Construct a curve defined in the polar coordinate system: ρ = 4 · sin 4φ.
№5 Construct a curve given by parametric equations (0 ≤ t ≤ 2π)
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