Concept:The distance between two points in a two-dimensional plane is given by \(\displaystyle d=\sqrt{(x_2-x_1)^2-(y_2-y_1)^2}\)Calculation:Given:Point (x, y) is equidistant from the points (2a, 0) and (0, 3a)\(\displaystyle d=\sqrt{(2a-x)^2+(0-y)^2}=\sqrt{(0-x)^2+(3a-y)^2}\)Squaring both sides, we get,? (2a - x)2 + y2 = x2 + (3a - y)2? 4a2 + x2 - 4ax + y2 = x2 + 9a2 + y2 - 6ay? 4a2 - 4ax = 9a2 - 6ay? 5a2 - 6ay + 4ax = 0? 5a - 6y + 4x = 0? 4x - 6y + 5a = 0? 4x - 6y + 5a = 0 is correct.