IDZ 4.1 - Option 1. 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
1.1 a) b = 15, F (-10, 0); b) a = 13, ε = 14/13; a) D: x = -4

2. Write the equation of the circle passing through these points and centered at the point A.
2.1 hyperbole Tops 12x2 - 13y2 = 156, A (0, -2)

3. Find the equation of a line, every point M which satisfies these criteria.
3.1 is spaced from the line x = -6 a distance twice than the point A (1, 3)

4. Build a curve given by the equation in polar coordinates.
4.1 ρ = 2sin4φ

5. Construct a curve given by parametric equations (0 ≤ t ≤ 2π)
5.1 x = 4cos3t y = 4sin3t