A point on the y-axis which is equidistant from the points A(6, 5) and B(-4, 3) is:

(0, 9)

Let point on y-axis is C( 0 , y )

From point to A(6 , 5) to (0 , y) ,

Distance from A = \(\sqrt { ( 0-6)² + ( y - 5 ) ² }\)

Distance from B = \(\sqrt { ( 0-4)² + ( y - 3 ) ² }\)

As, Point C is equidistance from Point A and B

\(\sqrt { ( 0-6)² + ( y - 5 )² }\) = \(\sqrt { ( 0-4)² + ( y - 3 ) ² }\)

36 + y² + 25 -10y = 16 + y² + 9 - 6y

y = 9

So, Point C ( 0 , 9 )

The correct answer is Option (1) → (0, 9)