ИДЗ 4.1 – Вариант 15. 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
1.15 a) A (-√17 / √3, 1/3), B (√21 / 2, 1/2); b) k = 1/2, ε = √5 / 2; a) D: y = -1

2. Write the equation of the circle passing through these points and centered at the point A.
2.15 Focuses hyperbola 5x2 - 11y2 = 55, A (0, 5)

3. Find the equation of a line, every point M which satisfies these criteria.
3.15 spaced from the line x = 9 in the region, four times less than that of the point A (-1, 2)

4. Build a curve given by the equation in polar coordinates.
4.15 ρ = 6sin4φ

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