Finding the Relation between x and y for Equidistant Point
In this problem, we are given two points A(2, 5) and B(-3, 7), and we need to find a relation between x and y such that the point P(x, y) is equidistant from points A and B.

Understanding the Concept of Equidistant Points
When a point is equidistant from two other points, it lies on the perpendicular bisector of the line segment joining the two points. This means that the distances from the equidistant point to the two given points are equal.

Deriving the Equation for Perpendicular Bisector
To find the equation of the perpendicular bisector of the line segment AB, we first need to find the midpoint of AB. The midpoint M = ((x1 + x2)/2, (y1 + y2)/2) = ((2 - 3)/2, (5 + 7)/2) = (-1/2, 6).
The slope of AB = (7 - 5)/(-3 - 2) = 2/-5 = -2/5.
Therefore, the slope of the perpendicular bisector = 5/2.
Using the point-slope form of the equation of a line, we get y - 6 = 5/2(x + 1/2).
Simplifying, we get y = 5/2x + 13.

Equating the Distance Formula
Now, we equate the distance from P(x, y) to A and B, using the distance formula.
For point A: √((x - 2)^2 + (y - 5)^2) = √((x + 3)^2 + (y - 7)^2).
Solving this equation will give us the relation between x and y for the point P(x, y) to be equidistant from points A and B.
In this way, we can find the relation between x and y such that the point P(x, y) is equidistant from the points A(2, 5) and B(-3, 7).