Find a relation between x and y, such that the point (x, y) is equidistant from the points (3,6) and (-3,4)

To find a relation between x and y such that the point (x, y) is equidistant from the points (3,6) and (-3,4), we can use the distance formula. The distance between two points (x1, y1) and (x2, y2) is given by:

d = sqrt[(x2 - x1)² + (y2 - y1)²]

We want the distance from (x, y) to (3,6) to be the same as the distance from (x, y) to (-3,4). So we can set up the following equation:

sqrt[(3 - x)² + (6 - y)²] = sqrt[(-3 - x)² + (4 - y)²]

Squaring both sides to get rid of the square root gives us:

(3 - x)² + (6 - y)² = (-3 - x)² + (4 - y)²

Expanding and simplifying gives us:

x = 2y - 5

So the relation between x and y such that the point (x, y) is equidistant from the points (3,6) and (-3,4) is x = 2y - 5.