IDZ 4.1 - Option 13. 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

1.13 a) a = 6, F (-4, 0); b) b = 3, F (7, 0), a) D: x = -7

• Write the equation of the circle passing through these points and centered at the point A.

2.13 The focus of the ellipse 16x2 + 41y2 = 656, A - its lower vertex

• Find the equation of a line, every point M which satisfies these criteria.

3.13 spaced from point A (-3, 3) at a distance of three times larger than that of the point B (5, 1)

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

5 4.13 ρ = (1 - sin2φ)

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

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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.