Question

A moving point is always equidistant from (-3,2) and the line 2x-y+2=0. What is the equation of its locus?

how do you solve this?

Answer 1

Sounds like the definition of a parabola: The locus of points equidistant from a point (the focus) and a line (the directrix). It will be a tilted parabola.

Good luck. Good exercise for you.