Conic Sections and Eccentricity

How is the curve classified as a conic section depending on the value of e?

Which geometric property of the curve is determined by the parameter a?

Express the distance from point P to the focus and the distance from P to the directrix using the polar coordinates of P and the constant a. Substitute these expressions into the definition and simplify the equation to obtain an expression for r.

A conic section is the locus of points whose distance from a fixed point (the focus) and a fixed line (the directrix) has a constant ratio.Consider the polar equation  . Answer the following questions. (1) Determine the type of conic represented by this curve and find its eccentricity e. Assume that the focus is located at the origin. (2) Find the equation of the directrix of this conic. (3) Express this curve in Cartesian coordinates (x,y).