IDZ 4.1 - Option 27. Decisions Ryabushko AP

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
1.27 a) A (-3, 0), B (1, √40 / 3); b) k = √2 / √3, ε = √15 / 3; a) D: y = 4

2. Write the equation of the circle passing through these points and centered at the point A.
2.27 Focuses hyperbola 4x2 - 5y2 = 20, A (0, -6)

3. Find the equation of a line, every point M which satisfies these criteria.
3.27 is spaced from the line x = - 7 at a distance of three times smaller than the point A (3, 1)

4. Build a curve given by the equation in polar coordinates.
4.27 ρ = 3cos2φ