Reshebnik Ryabushko. Solved IDZ 4.1, Option 18
Replenishment date: 28.06.2020
Content: 18v-IDZ4.1.rar (95.42 KB)
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Description
1. Make canonical equations: a) ellipse; b) hyperbole; c) parabolas (A, B are points lying on the curve, F is the focus, a is the major (real) semiaxis, b is the minor (imaginary) semiaxis, ε is the eccentricity, y = ± kx are the equations of the asymptotes of the hyperbola, D is the directrix curve, 2c - focal length
1.18 a) b = 5; ε = 12/13; b) k = 1/3, 2a = 6; c) axis of symmetry Oy and A (–9, 6)
2. Write down the equation of a circle passing through the indicated points and having a center at point A.
2.18 The left vertex of the hyperbola 5x2 - 9y2 = 45, A (0, –6)
3. Make an equation of a line, each point M of which satisfies the given conditions.
3.18 Distance from point A (0, −5) at a distance two times less than from the straight line x = 3
4. Construct the curve specified by the equation in the polar coordinate system.
4.18 ρ = 2 (1 - cos3φ)
5. Construct a curve given by parametric equations (0 ≤ t ≤ 2π)
5.18 x = 2cos3t y = 5sin3t
1.18 a) b = 5; ε = 12/13; b) k = 1/3, 2a = 6; c) axis of symmetry Oy and A (–9, 6)
2. Write down the equation of a circle passing through the indicated points and having a center at point A.
2.18 The left vertex of the hyperbola 5x2 - 9y2 = 45, A (0, –6)
3. Make an equation of a line, each point M of which satisfies the given conditions.
3.18 Distance from point A (0, −5) at a distance two times less than from the straight line x = 3
4. Construct the curve specified by the equation in the polar coordinate system.
4.18 ρ = 2 (1 - cos3φ)
5. Construct a curve given by parametric equations (0 ≤ t ≤ 2π)
5.18 x = 2cos3t y = 5sin3t
Additional Information
The solution is executed in Microsoft Word 2003. The document with the IDZ solution is archived in the WinRar program.