Assignment:
Q1. Write a polar equation of a conic with the focus at the origin and the given data.
1. Parabola, directrix x=4
2. Hyperbola, eccentricity 2, directrix y = -2
3. Ellipse, eccentricity 0.8, vertex (1, ∏/2)
Q2. (a)find the eccentricity,(b)identify the conic,(c)give an equation of the directrix, and (d)sketch the conic.
1.r = 6/(3+2 sinθ)
2.r = 4/(2-3 cosθ)
3.r = 5/(2-2 sinθ)
Provide complete and step by step solution for the question and show calculations and use formulas.