Find the equation for the graph of the path of a point​ P(x,y) that moves such that​ P(x,y) is the same distance from the point ​(14​,0) and the​ y-axis.

Answer 1

The focus is (14,0) and the directrix is x=0

SO, you have a parabola opening to the right, with 2p=14, and vertex at (7,0) halfway from directrix to focus:

y^2 = 28(x-7)

http://www.wolframalpha.com/input/?i=parabola+y%5E2+%3D+28(x-7)