IDZ 4.1 - Option 10. 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

1.10 a) ε = 7/8, A (8, 0); b) A (3, -√3 / √5), B (√13 / √5, 6); a) D: y = 4

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

2.10 O (0, 0), A - the vertex of the parabola y2 = - (x + 5) / 2

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

3.10 The ratio of the distances from point M to point A (-3, 5) and B (4, 2) is 1/3

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

4.10 ρ = 4sin4φ

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

5.10 x = 3cost y = 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.