Step 1: Calculate the distance
Given: is equidistant from and .
i.e.,
The distance between two points and :
[ Distance formula ]
The distance between the points and is,
Step 2: Calculate the distance
The distance between the points and is,
Step 3: Prove the required equation
According to the question, the point is equidistant from the points and .
i.e.,
[Squaring on both sides]
Hence, it is proved that .