IDZ 4.1 - Option 28. Decisions Ryabushko AP

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• Create the canonical equations: a) of the ellipse; b) hyperbole; c) the parabola (A, B - points on the curve, F - focus, and - big (real) Semi, b - small (imaginary) half, ε - eccentricity, y = ± kx - hyperbolic equations of the asymptotes, D - Headmistress curve, 2c - focal length

1.28 a) ε = 5/6, A (0, -√11); b) A (√32 / √3, 1), B (√8, 0); a) D: y = -3

• Write the equation of the circle passing through these points and centered at the point A.

2.28 B (3, 4), and - the vertex of the parabola y2 = (x + 7) / 4

• Find the equation of a line, every point M which satisfies these criteria.

3.28 The ratio of the distances from point M to point A (3, -5) and B (4, 1) is equal to 1/4

• Build a curve given by the equation in polar coordinates.

4.28 ρ = 2sin3φ

• Construct a curve given by parametric equations (0 ≤ t ≤ 2π)

5.28 x = 4cost y = 4 (1-sint)

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Detailed solution. Designed in PDF format for easy viewing of IDZ solutions on smartphones and PCs. In MS Word (doc format) sent additionally.