Equidistant set Let S be the square centered at the origin

Solution 50REStep 1 of 2:In this problem we need to describe and sketch the set of points that are equidistant from the square and the origin.Given : Let S be the square centered at the origin with vertices (a , a) and (a , a)Clearly , the vertices are ; ( a, a) , (a , -a) , (-a, a) and (-a , -a).Let us consider ( u , v) be any point which is equidistant from the square and the origin.Now , the square of the side is ; y - a = (x -a) Y - a = (x - a) x - a = 0 . NOTE: The equation of a line passing through two points () and () is (y - ) = m( x - , where m = Similarly the remaining sides are ; x + a= 0 , y - a = 0 and y+ a = 0.Hence , ( u , v) be any point which is equidistant from the square of the side (x- a) = 0 , and the origin is : = , squaring on both sides we get : , since cancel out the like terms . Therefore , the equation of is same as Clearly , the above equation represents a parabola.