IDZ Ryabushko 4.1 Variant 9
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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 (0; √3); B (√14 / 3; 1); b) k = √21 / 10; ε = 11/10; c) D: y = - 4.
No. 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 = 80; A (0; –4).
№3 Draw up the equation of the line, each point M of which satisfies the given conditions. It is spaced from the line y = 7 at a distance five times greater than from point A (4; –3).
№4 Construct a curve defined in the polar coordinate system: ρ = 4 · sin 3φ.
№5 Construct a curve given by parametric equations (0 ≤ t ≤ 2π)
No. 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 = 80; A (0; –4).
№3 Draw up the equation of the line, each point M of which satisfies the given conditions. It is spaced from the line y = 7 at a distance five times greater than from point A (4; –3).
№4 Construct a curve defined in the polar coordinate system: ρ = 4 · sin 3φ.
№5 Construct a curve given by parametric equations (0 ≤ t ≤ 2π)
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