P(x,y) is to be constructed so that its distance from the road at the line with equation y=1.5 and from a supply depot at f(6,4.5), are the same. Find the equation of the possible locations of P

Answer 1

I think what is being asked here is to find the locus of points equidistant from the point (6,4.5) and the line

y=1.5,

The answer is a parabola with vertex (6,3) the equation of which is y=(x-6)² + 3.

Why?

Because by (at least one) definition a parabola is the locus of points equidistant from a point and a line,