Reshebnik Ryabushko. Solved IDZ 4.1, Option 19

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
1.19 a) a = 9, F (7, 0); b) b = 6, F (12, 0), c) D: x = –1/4

2. Write down the equation of a circle passing through the indicated points and having a center at point A.
2.19 Focuses of the ellipse 24x2 + 25y2 = 600, A is its top vertex

3. Make an equation of a line, each point M of which satisfies the given conditions.
3.19 Distance from point A (4, −2) at a distance half as much as from point B (1, 6)

4. Construct the curve specified by the equation in the polar coordinate system.
4.19 ρ = 3 (1 - cos4φ)

5. Construct a curve given by parametric equations (0 ≤ t ≤ 2π)
5.19 x = 4cos2t y = sin2t