Geometric Condition in a Rectangle

Very Hard Geometry Shapes And Properties

In the coordinate plane, consider a rectangle with vertices at points A(2, 3), B(2, 7), C(8, 7), and D(8, 3). A point P lies inside this rectangle. It is given that the distance from point P to vertex A is equal to the distance from point P to vertex C. If point P is located at (x, y), which of the following equations must be satisfied?

$(x - 2)^2 + (y - 3)^2 = (x - 8)^2 + (y - 7)^2$