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IDZ Ryabushko 4.1 Variant 23
Uploaded: 24.04.2024
Content: 4.1 - 23.pdf 93,45 kB
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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) 2a = 50; ε = 3/5; b) k = √29 / 14; 2c = 30; c) the axis of symmetry of Oy and A (4; 1).
№2 Write down the equation of a circle passing through the indicated points and having a center at point A. Given: Right focus of the ellipse x2 + 4y2 = 12; A (2; –7).
№3 Draw up the equation of the line, each point M of which satisfies the given conditions. The sum of the squares of the distances from point M to points A (–5; 3) and B (2; –4) is 65.
№4 Construct a curve defined in the polar coordinate system: ρ = 4 · (1 + cos 2φ).
№5 Construct a curve given by parametric equations (0 ≤ t ≤ 2π)
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