IDZ 4.1 - Option 24. 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
1.24 a) b = 2√15, ε = 7/8, b) k = 5/6, 2a = 12; c) symmetry axis Oy and A (-2, 3√2)

2. Write the equation of the circle passing through these points and centered at the point A.
2.24 The right top hyperbole 40x2 - 81y2 = 3240, A (-2, 5)

3. Find the equation of a line, every point M which satisfies these criteria.
3.24 spaced from point A (3, 4) at a distance of three times greater than the straight line x = 5

4. Build a curve given by the equation in polar coordinates.
4.24 ρ = 1 / (2 - cos2φ)

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