# IDZ 4.1 - Option 29. Decisions Ryabushko AP

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Content: 29v-IDZ4.1.doc 209 kB

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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
1.29 a) 2a = 30, ε = 17/15, b) k = √17 / 8, 2c = 18; c) the Oy axis of symmetry and A (4, -10)

2. Write the equation of the circle passing through these points and centered at the point A.
2.29 Left focus of the ellipse 13x2 + 49y2 = 637, A (1, 8)

3. Find the equation of a line, every point M which satisfies these criteria.
3.29 Sum of squares of the distances from point M to point A (-1, 2) and B (3, -1) is 18.5

4. Build a curve given by the equation in polar coordinates.
4.29 ρ = 2 / (2 - cosφ)

5. Construct a curve given by parametric equations (0 ≤ t ≤ 2π)
5.29 x = cost y = 3sint