IDZ Ryabushko 4.1 Option 11

IDZ Ryabushko 4.1 Option 11

Ryabushko IDZ Solution 4.1 - Option 11

Section: Chapter 4. Lines and Surfaces
Topic: Second-order curves
Description: Canonical equations of an ellipse, hyperbola, parabola. Equation of a circle. Composing line equations based on geometric conditions. Plotting curves in polar and parametric coordinates.

Tasks:
1. Compose canonical equations: a) ellipse; b) hyperbola; c) parabola; A; B - points lying on the curve; F - focus; a - semi-major (real) axis; b- semi-minor (imaginary) axis; ε - eccentricity; y = ± k x - equations of hyperbola asymptotes; D - directrix of the curve; 2c- focal distance.
2. Write the equation of a circle passing through the specified points and having its center at point A.
3. Compose the equation of a line where each point M satisfies the given conditions. It is at a distance from the line x = –6 that is twice as large; as from point A(1;3).
4. Plot a curve given in polar coordinates: ρ = 2·sin 4φ.
5. Plot a curve given by parametric equations ( 0 ≤ t ≤ 2π )

The completed solution includes:
• Full solution of all 5 tasks of the option
• Detailed explanations for each step
• All formulas and calculations
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