If a point P(x, y) is the equidistant from the points A(2,3) and B(6,1), find the equation of locus of moving point P. please answer it and I will mark your answer as the brainliest..please..!!!

Step-by-step explanation:

A locus can be defined as a curve or figure formed by all the points satisfying a particular equation of the relation between coordinates.

The condition stated in the question is such that a generic (x,y) point of the curve is equidistant from the points A(2,3) and B(6,1).

The distance d1 from (x,y) to (2,3) is:

The distance d2 from (x,y) to (6,1) is:

Since d1=d2:

Squaring both sides:

Operating:

Simplifying all the squares:

Moving the variables to the left side and the numbers to the right side:

Simplifying:

Dividing by 4:

Or, equivalently:

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step-by-step explanation:

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