Find the equation for the set of all points p(x,y) if it is equidistant from (2,3) and the x-axis.

Answer 1

Your sentence is the definition of a parabola with
focus = (2,3)
directrix y=0
Now recall that the parabola
x^2 = 4py has
vertex (0,0)
focus (0,p)
directrix y = -p

So, your parabola has
vertex at (2,3/2) with p = 3/2
So, its equation is

(x-2)^2 = 6(y-3/2)

See the graph at

https://www.wolframalpha.com/input/?i=parabola+(x-2)%5E2+%3D+6(y-3%2F2)