ИДЗ 4.1 – Вариант 5. 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
1.5 a) 2a = 22, ε = √57 / 11, b) k = 2/3, 2c = 10√13; a) symmetry axis Ox and A (27: 9)

2. Write the equation of the circle passing through these points and centered at the point A.
2.5 foci of the ellipse 9x2 + 25y2 = 1, A (0, 6)

3. Find the equation of a line, every point M which satisfies these criteria.
3.5 Sum of squares of the distances from point M to point A (4, 0) and B (-2, 2) is equal to 28

4. Build a curve given by the equation in polar coordinates.
4.5 ρ = 2 / (1 + cosφ)

5. Construct a curve given by parametric equations (0 ≤ t ≤ 2π)
5.5 x = 4cost y = 5sint

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