IDZ 4.1 - Option 22. 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

1.22 a) ε = 2/3, A (-6, 0); b) A (√8, 0), B (√20 / 3, 2); a) D: y = 1

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

2.22 B (2 to 5), A - the vertex of the parabola x2 = - 2 (y + 1)

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

3.22 The ratio of the distances from point M to point A (3, -2) and B (4, 6) is equal to 3/5

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

4.22 ρ = 2cos4φ

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

5.22 x = cost y = 3 (2-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.