1. A point P(x,y) is given equidistant from the points A(a+b,b-a) and B(a-b,a+b), then prove that bx = ay also find the locus of the variable point Z(a cos (theta), b sin (theta)), where (theta) is a variable quantity. 2. T0 prove that ax = by 3. In an attempt towards implementing what's given, i applied the distance formula knowing the fact that it will be a lengthy solution but still i did not came up with an answer. and the second part of the question, i am still doubtful about how to find a locus to a variable point. The value of theta is variable so, the x-coordinate and y-coordinate will oscillate from [-1,1].