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IDZ Ryabushko 4.1 Variant 22

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IDZ Ryabushko 4.1 Variant 22

№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) ε = 2/3; A (–6; 0; b) A (√8; 0); c) D: y = 1.
b) Invalid condition. Point coordinates are incorrect. Not resolved

№2 Write down the equation of a circle passing through the indicated points and having a center at point A. Given: B (2; –5); A is the vertex of the parabola x2 = –2 · (y +1).

№3 Draw up the equation of a line, each point M of which satisfies the conditions: The ratio of the distances from point M to points A (3; –2) and B (4; 6) is 3/5.

№4 Construct a curve defined in the polar coordinate system: ρ = 2 · cos 4φ.

№5 Construct a curve given by parametric equations (0 ≤ t ≤ 2π)

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