Option 2 DHS 4.1

DHS - 4.1
№1.2. Make the canonical equation: a) an ellipse; b) hyperbole; c) parabolas; BUT; B - points lying on the curve; F - focus;
and - the big (real) semi-axis; b- small (imaginary) semi-axis; ε - eccentricity; y = ± k x - equations of the asymptotes of the hyperbola; D is the director of the curve; 2c is the focal length. Given: a) b = 2; F (4√2; 0); b) a = 7; ε = √85 / 7; c) D: x = 5.
№ 2.2. Write the equation of a circle passing through the indicated points and having a center at A. Given: the vertices of the hyperbola 4x2 - 9y2 = 36; A (0; 4).
No. 3.2. Make an equation of the line, each point M of which satisfies the given conditions. It is separated from the line x = –2 at a distance twice as large; than from point A (4; 0).
No. 4.2. Build a curve defined in the polar coordinate system: ρ = 2 · (1 - sin 2φ).
No. 5.2. Build a curve defined by parametric equations (0 ≤ t ≤ 2π)