IDZ Ryabushko 4.1 Variant 24
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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 = 2√15; ε = 7/8; b) k = 5/6; 2a = 12; c) The axis of symmetry of Oy and A (-2; 3√2).
№2 Write down the equation of a circle passing through these points and having a center at point A (-2; 5). The right vertex of the hyperbola is 40x2-81y2 = 3240.
№3 Draw up the equation of the line, each point M of which satisfies the given conditions. It is spaced from the point A (3; -4) at a distance three times larger than from the line x = 5
№4 Construct a curve defined in the polar coordinate system: ρ = 1 / (2 - cos2φ).
№5 Construct a curve given by parametric equations (0 ≤ t ≤ 2π)
№2 Write down the equation of a circle passing through these points and having a center at point A (-2; 5). The right vertex of the hyperbola is 40x2-81y2 = 3240.
№3 Draw up the equation of the line, each point M of which satisfies the given conditions. It is spaced from the point A (3; -4) at a distance three times larger than from the line x = 5
№4 Construct a curve defined in the polar coordinate system: ρ = 1 / (2 - cos2φ).
№5 Construct a curve given by parametric equations (0 ≤ t ≤ 2π)
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