First, make a sketch . . . Find the equation of the locus of the point P(x,y) which moves so that
it is always equidistant from the point and the line
-4+ - - - * - - - L
The distance from is: .
The distance from to line is: .
Since , we have: .
That is the equation of the locus, so technically, we're done.
. . But, of course, we are expected to simplify our equation.
. . Square both sides: .
. . Expand: .
. . And we have: .
. . Add 1 to both sides: .
. . Factor: .
The locus is a parabola.
. . It opens upward, and its vertex is at