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IDZ Ryabushko 4.1 Variant 14

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IDZ Ryabushko 4.1 Variant 14

№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 = 7; F (5; 0); b) a = 11; ε = 12/11; c) D: x = 10.

№2 Write down the equation of a circle passing through the indicated points and having a center at point A. Given: The top of the hyperbola 2x2–9y2 = 18; 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 x = 8 at a distance two times larger than from point A (–1; 7).

№4 Construct a curve defined in the polar coordinate system: ρ = 3 · (2 ​​- cos 2φ).

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

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