IDZ Ryabushko 4.1 Variant 15
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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 (-√17 / 3; 1/3); B (√21 / 2; 1/2); b) k = 1/2; ε = √5 / 2; c) D: y = - 1.
№2 Write down the equation of a circle passing through the indicated points and having a center at point A. Given: Focuses of the hyperbole 5x2 - 11y2 = 55; A (0; 5).
№3 Draw up the equation of the line, each point M of which satisfies the given conditions. It is spaced from the line x = 9 at a distance four times smaller than from point A (–1; 2).
№4 Construct a curve defined in the polar coordinate system: ρ = 6 · sin 4φ.
№5 Construct a curve given by parametric equations (0 ≤ t ≤ 2π)
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 (-√17 / 3; 1/3); B (√21 / 2; 1/2); b) k = 1/2; ε = √5 / 2; c) D: y = - 1.
№2 Write down the equation of a circle passing through the indicated points and having a center at point A. Given: Focuses of the hyperbole 5x2 - 11y2 = 55; A (0; 5).
№3 Draw up the equation of the line, each point M of which satisfies the given conditions. It is spaced from the line x = 9 at a distance four times smaller than from point A (–1; 2).
№4 Construct a curve defined in the polar coordinate system: ρ = 6 · sin 4φ.
№5 Construct a curve given by parametric equations (0 ≤ t ≤ 2π)
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