If P be a point equidistant from points A (3,4) and B (5,-2) and area of `DeltaPAB` is 10 square units, then find the co-ordinates of point P.

Explanation

To find the coordinates of point P that is equidistant from points A (3, 4) and B (5, -2) and forms a triangle with area 10 square units, we can follow these steps:

### Step 1: Set up the distance condition
Since point P is equidistant from points A and B, we can express this condition mathematically. Let the coordinates of point P be (x, y). The distances PA and PB can be expressed as:

- Distance PA:
\[
PA = \sqrt{(x - 3)^2 + (y - 4)^2}
...