ИДЗ 4.1 – Вариант 30. 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
1.30 a) b = 2√2, ε = 7/9, b) k = √2 / 2, 2a = 12; c) the Oy axis of symmetry and A (-45, 15)

2. Write the equation of the circle passing through these points and centered at the point A.
2.30 The right focus hyperbole 57x2 - 64y2 = 3648, A (2, 8)

3. Find the equation of a line, every point M which satisfies these criteria.
3.30 spaced from point A (1, 5) at a distance of four times less than that of the straight line x = -1

4. Build a curve given by the equation in polar coordinates.
4.30 ρ = 2 - cos2φ

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

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