The given points are A(-5, 4) and B(-1, 6).
Let the given point be P(x, y).
P is equidistant from A and B, so PA = PB or PA2 = PB2
Using distance formula, we have:
(x+5)2 + (y-4)2 = (x+1)2 + (y-6)2
x2 + 25 + 10x + y2 + 16 - 8y = x2 + 1 + 2x + y2 + 36 - 12y
8x + 4y + 4 = 0
2x + y + 1 = 0
This is the condition for the point P to be equidistant from A and B.
This is a linear equation in the variables x and y. So, there will be infinitely many points (x, y) satisfying this equation.
Thus, there will be infinitely many points which will be equidistant from A and B.
We hope that clarifies your query.