IDZ Ryabushko 4.1 Option 5

IDZ Ryabushko 4.1 Option 5

Solution IDZ Ryabushko 4.1 - Option 5

Section: Chapter 4. Lines and Surfaces
Topic: Second order lines
Description: Canonical equations of ellipse, hyperbola, parabola. Equation of a circle. Drawing up equations of lines based on geometric conditions. Construction of 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 – semimajor (real) axis, b – semiminor (imaginary) axis, ε – eccentricity, y = ±kx – equations of hyperbola asymptotes, D – directrix of the curve, 2c – focal distance).
2. Write the equation of a circle passing through the given points and having its center at point A.
3. Compose an equation of a line, each point M of which satisfies the given conditions.
4. Construct a curve given by an equation in the polar coordinate system.
5. Construct a curve given by parametric equations (0 ≤ t ≤ 2π).

The complete solution includes:
• Complete solution to all 5 variant tasks
• Detailed explanations for each step
• All formulas and calculations
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