Version 4.1 Collection of 16 DHS DHS Ryabushko

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DHS - 4.1
№1.16. Be the canonical equation of: a) the ellipse; b) hyperbole; c) a parabola; A; The - the point lying on the curve; F - focus;
and - a big (real) sex; b- small (imaginary) sex; ε - eccentricity; y = ± kx - the equations of the asymptotes of the hyperbola; D - the headmistress of the curve; 2c- focal length. Given: a) ε = 3/5; A (0, 8); b) A (√6; 0); B (-2√2; 1); a) D: y = 9.
№2.16. Write the equation of the circle passing through these points and centered at the point A. Given: B (1, 4); A - the vertex of the parabola y2 = (x - 4) / 3.
№3.16. Write the equation of a line, every point M which satisfies these criteria. The ratio of the distance from point M to point A (2; 4) and B (3, 5) is equal to 2/3.
№4.16. Build a curve given in polar coordinates: ρ = 2 · cos 6φ.
№5.16. Build a curve given by parametric equations (0 ≤ t ≤ 2π)