IDZ Ryabushko 4.1 Variant 27
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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) A (–3; 0); B (1; √40 / 3); b) k = √2 / 3; ε = √15 / 3; c) D: y = 4.
№2 Write down the equation of a circle passing through the indicated points and having a center at point A. Given: Foci of the hyperbola 4x2 - 5y2 = 20; A (0; –6).
№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 = - 7 at a distance three times smaller than from point A (3; 1).
№4 Construct a curve defined in the polar coordinate system: ρ = 3 · cos 2φ.
№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: Foci of the hyperbola 4x2 - 5y2 = 20; A (0; –6).
№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 = - 7 at a distance three times smaller than from point A (3; 1).
№4 Construct a curve defined in the polar coordinate system: ρ = 3 · cos 2φ.
№5 Construct a curve given by parametric equations (0 ≤ t ≤ 2π)
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