locus: PA=ePL

A point P moving in such a manner that distance from given point A is equal to e times of its distance from the given line L. Determine the locus equation of the moving point P. 動點P至定點A之距離=離心率e*P至直線L之距離,求P之軌跡方程式

Please give it a try: 1. e=1 2. e<1 3. e>1 What kind of curve is it for each case?