IDZ Ryabushko 4.1 Variant 28
Content: 4.1 - 28.pdf (83.04 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 = 5/6; A (0; -√11); b) A (√32 / 3; 1); B (√8; 0); c) D: y = - 3.
№2 Write down the equation of a circle passing through the indicated points and having a center at point A. Given: B (3; 4); A is the apex of the parabola; y2 = (x + 7) / 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 (3; –5) and B (4; 1) is 1/4.
№4 Construct a curve defined in the polar coordinate system: ρ = 2 · sin 3φ.
№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: B (3; 4); A is the apex of the parabola; y2 = (x + 7) / 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 (3; –5) and B (4; 1) is 1/4.
№4 Construct a curve defined in the polar coordinate system: ρ = 2 · sin 3φ.
№5 Construct a curve given by parametric equations (0 ≤ t ≤ 2π)
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