IDZ Ryabushko 4.1 Variant 4
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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 = √21 / 5; A (–5; 0); b) A (√80; 3); B (4√6; 3√2); c) D: y = 1.
No. 2 Write down the equation of a circle passing through the indicated points and having a center at point A. Given: 0 (0; 0); A is the vertex of the parabola y2 = 3 (x - 4).
№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; 3) and B (–1; 2) is 3/4.
№4 Construct a curve defined in the polar coordinate system: ρ = 3 · sin 6φ.
№5 Construct a curve given by parametric equations (0 ≤ t ≤ 2π)
No. 2 Write down the equation of a circle passing through the indicated points and having a center at point A. Given: 0 (0; 0); A is the vertex of the parabola y2 = 3 (x - 4).
№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; 3) and B (–1; 2) is 3/4.
№4 Construct a curve defined in the polar coordinate system: ρ = 3 · sin 6φ.
№5 Construct a curve given by parametric equations (0 ≤ t ≤ 2π)
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