ИДЗ 4.1 – Вариант 22. Решения Рябушко А.П.

1. 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

2. 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)

3. 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

4. Build a curve given by the equation in polar coordinates.
4.22 ρ = 2cos4φ

5. Construct a curve given by parametric equations (0 ≤ t ≤ 2π)
5.22 x = cost y = 3 (2-sint)

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