# IDZ 4.1 - Option 11. Decisions Ryabushko AP

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Content: 11v-IDZ4.1.doc 207 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
1.11 a) 2a = 24, ε = √22 / 6, b) k = √2 / √3, 2c = 10; a) symmetry axis Ox and A (-7, -7)

2. Write the equation of the circle passing through these points and centered at the point A.
2.11 The right focus of the ellipse 33x2 + 49y2 = 1617, A (1, 7)

3. Find the equation of a line, every point M which satisfies these criteria.
3.11 Sum of squares of the distances from point M to point A (-5, -1) and B (3, 2) is equal to 40.5

4. Build a curve given by the equation in polar coordinates.
4.11 ρ = 3 (cosφ + 1)

5. Construct a curve given by parametric equations (0 ≤ t ≤ 2π)
5.11 x = 2cost y = 4sint