IDZ 4.1 - Option 24. 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

1.24 a) b = 2√15, ε = 7/8, b) k = 5/6, 2a = 12; c) symmetry axis Oy and A (-2, 3√2)

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

2.24 The right top hyperbole 40x2 - 81y2 = 3240, A (-2, 5)

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

3.24 spaced from point A (3, 4) at a distance of three times greater than the straight line x = 5

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

4.24 ρ = 1 / (2 - cos2φ)

• 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.