Reshebnik Ryabushko. Solved IDZ 4.1, Option 16

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
1.16 a) ε = 3/5, A (0, 8); b) A (√6), B (−0√2); c) D: y = 2

2. Write down the equation of a circle passing through the indicated points and having a center at point A.
2.16 B (1, 4), A is the vertex of the parabola y2 = (x - 4) / 3

3. Make an equation of a line, each point M of which satisfies the given conditions.
3.16 The ratio of the distances from point M to points A (2, −4) and B (3, 5) is 2/3

4. Construct the curve specified by the equation in the polar coordinate system.
4.16ρ = 2cos6φ

5. Construct a curve given by parametric equations (0 ≤ t ≤ 2π)
5.16 x = 2cost y = 2 (1-sint)