IDZ 4.1 - Option 11. Decisions Ryabushko AP

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• 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)

• 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)

• 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

• Build a curve given by the equation in polar coordinates.

4.11 ρ = 3 (cosφ + 1)

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

5.11 x = 2cost y = 4sint

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Detailed solution. Designed in PDF format for easy viewing of IDZ solutions on smartphones and PCs. In MS Word (doc format) sent additionally.