ИДЗ 4.1 – Вариант 25. 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
1.25 a) a = 13, F (-5, 0); b) b = 4, F (-7, 0), a) D: x = -3/8

2. Write the equation of the circle passing through these points and centered at the point A.
2.25 foci of the ellipse x2 + 10y2 = 90, A - its lower vertex

3. Find the equation of a line, every point M which satisfies these criteria.
3.25 spaced from point A (5, 7) at a distance of four times greater than that of the point B (-2, 1)

4. Build a curve given by the equation in polar coordinates.
4.25 ρ = 4 (1 - sinφ)

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

Detailed solution. Designed in PDF format for easy viewing of IDZ solutions on smartphones and PCs. In MS Word (doc format) sent additionally.