Equidistant set Show that the set of points equidistant from a circle and a line not passing through the circle is a parabola.

Solution 87AEThis graph is shown below Let C (c,0) be any point on the circleAnd P (x,y) be any point on the locusAnd let x = -c is a lineNow by given data CP = PM CP2 = PM2 (x-c)2 +y2 = (x+c)2 y2 = 4cxLocus of the point P (x,y) is a parabolaThe set of points equidistant from a circle and a line not passing through the circle is a parabola.