Reshebnik Ryabushko. Solved IDZ 4.1, Option 2
Replenishment date: 15.12.2022
Content: 2v-IDZ4.1.rar (88.18 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
1.2 a) b = 2, F (4√2, 0); b) a = 7, ε = √85 / 7; c) D: x = 5
2. Write down the equation of a circle passing through the indicated points and having a center at point A.
2.2 Vertices of hyperbola 4x2 - 9y2 = 36, A (0, 4)
3. Make an equation of a line, each point M of which satisfies the given conditions.
3.2 Distance from the straight line x = −2 at a distance two times greater than from the point A (4, 0)
4. Construct the curve specified by the equation in the polar coordinate system.
4.2 ρ = 2 (1 - sin2φ)
5. Construct a curve given by parametric equations (0 ≤ t ≤ 2π)
5.2 x = 2cos3t y = 2sin3t
1.2 a) b = 2, F (4√2, 0); b) a = 7, ε = √85 / 7; c) D: x = 5
2. Write down the equation of a circle passing through the indicated points and having a center at point A.
2.2 Vertices of hyperbola 4x2 - 9y2 = 36, A (0, 4)
3. Make an equation of a line, each point M of which satisfies the given conditions.
3.2 Distance from the straight line x = −2 at a distance two times greater than from the point A (4, 0)
4. Construct the curve specified by the equation in the polar coordinate system.
4.2 ρ = 2 (1 - sin2φ)
5. Construct a curve given by parametric equations (0 ≤ t ≤ 2π)
5.2 x = 2cos3t y = 2sin3t
Additional Information
The solution is executed in Microsoft Word 2003. The document with the IDZ solution is archived in the WinRar program.