Polar equations for conic sections Graph the following conic sections, labeling vertices, foci, directrices, and asymptotes (if they exist). Give the eccentricity of the curve. Use a graphing utility to check your work.
\(r=\frac{3}{1-2 \cos \theta}\)
Solution 34REGiven polar equation is r = We have to find the vertices foci directions and asymptotes of the conicWe know that conic section with a focus at the origin and eccentricity e has the polar Equation r = Given equation is r = Compare this equation with (1) we get e =2, ed Hence given conic system represents a hyperbolaLet in the given equation to get the vertices.Vertices are (-3, 0 ) in the vertex in cartesian coordinates Center is (-2,0 )One directrix is x = - 3/2Distance from the center to directrix x = - 3/2 is 2-3/2 - ½Hence another directrix is x = - 2- = x = - One focus is (0,0 ) is is 2 units distance from the centre another focus is (-4,0)
