ИДЗ 4.1 – Вариант 23. 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
1.23 a) 2a = 50, ε = 3/5, b) k = √29 / 14 2c = 30; c) the Oy axis of symmetry and A (4, 1)

2. Write the equation of the circle passing through these points and centered at the point A.
2.23 The right focus of the ellipse x2 + 4y2 = 12, A (2, -7)

3. Find the equation of a line, every point M which satisfies these criteria.
3.23 Sum of squares of the distances from point M to point A (-5, 3) and B (2, 4) is 65

4. Build a curve given by the equation in polar coordinates.
4.23 ρ = 4 (1 + cos2φ)

5. Construct a curve given by parametric equations (0 ≤ t ≤ 2π)
5.23 x = 9cost y = 5sint

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