Find a relation between x and y such thai the point P(x, y) is equidistant from the points A(2, 5) and B(-3, 7).

It is given that: point P(x, y) is equidistant from the points A(2, 5) and B(-3, 7)

Squaring both sides,
x² + y² - 4x - 10y + 29
= x² + y² + 6x - 14y + 58
⇒ -4x - 6x - 10y + 14y + 29 - 58 = 0
⇒    -10x + 4y - 29 = 0
⇒    -(10x - 4y + 29) = 0
⇒    10x — 4y + 29 = 0
⇒    10x -4y + 29 = 0. Ans.