IDZ Ryabushko 4.1 Variant 19
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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 = 9; F (7; 0); b) b = 6; F (2; 0); c) D: x = - 1/4.
№2 Write down the equation of a circle passing through the indicated points and having a center at point A. Foci of the ellipse 24x2 + 25y2 = 600; A is its top peak.
№3 Draw up the equation of the line, each point M of which satisfies the given conditions. It is separated from point A (4; –2) at a distance two times smaller than from point B (1; 6).
№4 Construct a curve defined in the polar coordinate system: ρ = 3 · (1 - cos4φ).
№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 = 9; F (7; 0); b) b = 6; F (2; 0); c) D: x = - 1/4.
№2 Write down the equation of a circle passing through the indicated points and having a center at point A. Foci of the ellipse 24x2 + 25y2 = 600; A is its top peak.
№3 Draw up the equation of the line, each point M of which satisfies the given conditions. It is separated from point A (4; –2) at a distance two times smaller than from point B (1; 6).
№4 Construct a curve defined in the polar coordinate system: ρ = 3 · (1 - cos4φ).
№5 Construct a curve given by parametric equations (0 ≤ t ≤ 2π)
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