Question

Find a point on the y-axis which is equidistant from the points (5, 2) and (-4, 3).

Answer 1

Let the co-ordinates of the required point on y-axis be P (0, y).
The given points are A (5, 2) and B (-4, 3).
Given, PA = PB
PA² = PB²
(0 -5)² + (y -2)² = (0 + 4)² + (y - 3)²
25 + y² + 4 - 4y = 16 + y² + 9 - 6y
2y = -4
y = -2
Thus, the required point is (0, -2).