Option 3 idz 4.1 Collection of idz ryabushko

Tasks, etc - 4.1
No. 1.3. Make a canonical equation: a) ellipse; b) hyperbola; C) parabola; A; C - points lying on the curve; F - focus; a - large ( real ) half - axis; b - small ( imaginary) half - axis; ε - eccentricity; y = ± k x - equations of the hyperbola´s asymptote; D-the curve´s directrix; 2c-focal distance. Given: a) A(3;0); B(2;√5/3); b) k = 3/4; ε = 5/4; C) D: y = – 2.
No. 2.3. Write the equation of a circle passing through the specified points and having the center at point A. Given: hyperbola Foci 24y2-25x2 = 600; A (-8;0).
No. 3.3. Create an equation for a line, each point M of which satisfies the specified conditions. The distance from the straight line y = -2 is three times greater than from point A (5; 0).
No. 4.3. Build a curve specified in the polar coordinate system: p = 2·sin 2φ.
#5.3. Construct a curve defined by parametric equations ( 0 ≤ t ≤ 2π )