IDZ 4.1 - Option 25. 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

1.25 a) a = 13, F (-5, 0); b) b = 4, F (-7, 0), a) D: x = -3/8

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

2.25 foci of the ellipse x2 + 10y2 = 90, A - its lower vertex

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

3.25 spaced from point A (5, 7) at a distance of four times greater than that of the point B (-2, 1)

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

4.25 ρ = 4 (1 - sinφ)

• 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.