IDZ Ryabushko 4.1 Variant 20

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IDZ Ryabushko 4.1 Variant 20

№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 = 5; F (–10; 0); b) a = 9; ε = 4/3; c) D: x = 12.

№2 Write down the equation of a circle passing through the indicated points and having a center at point A. Given: The right vertex of the hyperbola 3x2 - 16y2 = 48; A (1 3).

№3 Draw up the equation of the line, each point M of which satisfies the given conditions. It is spaced from the line x = –7 at a distance three times smaller than from point A (1; 4).

№4 Construct a curve defined in the polar coordinate system: ρ = 5 · (2 ​​- sin φ).

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


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