IDZ Ryabushko 4.1 Variant 8
Content: 4.1 - 8.pdf (78.48 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) b = 4; F (9; 0); b) a = 5; ε = 7/5; c) D: x = 6.
№2 Write down the equation of a circle passing through the top of the hyperbola x2 - 16y2 = 64 and having a center at point A (0; –2).
№3 Draw up the equation of the line, each point M of which satisfies the given conditions. It is spaced from the straight line x = - 5 at a distance three times as large; than from point A (6; 1).
№4 Construct a curve defined in the polar coordinate system: ρ = 3 · (1 - cos2φ).
№5 Construct a curve given by parametric equations (0 ≤ t ≤ 2π)
№2 Write down the equation of a circle passing through the top of the hyperbola x2 - 16y2 = 64 and having a center at point A (0; –2).
№3 Draw up the equation of the line, each point M of which satisfies the given conditions. It is spaced from the straight line x = - 5 at a distance three times as large; than from point A (6; 1).
№4 Construct a curve defined in the polar coordinate system: ρ = 3 · (1 - cos2φ).
№5 Construct a curve given by parametric equations (0 ≤ t ≤ 2π)
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