IDZ 4.1 - Option 16. 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

1.16 a) ε = 3/5, A (0, 8); b) A (√6, 0), B (-2√2, 1); a) D: y = 9

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

2.16 B (1, 4), and - the vertex of the parabola y2 = (x - 4) / 3

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

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

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

4.16 ρ = 2cos6φ

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

5.16 x = 2cost y = 2 (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.