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

Let the point be Y(0,y) and the other two points given as A(6,5) and B(– 4,3)

Given YA = YB

By distance formula, as shown below:

YA = √{(6 – 0)² + (5 – y)²}

= √{(6)² + (5 – y)²}

= √{36 + 25 + y² – 10y}

⇒ YA = √{61 + y² – 10y}

YB = √{(– 4 – 0)² + (3 – y)²}

= √{(– 4)² + (9 + y² – 6y)}

= √{16 + 9 + y² – 6y}

⇒ YB = √{25 + y² – 6y}

Now, YA = YB

Squaring both sides, we get,

(61 + y² – 10y) = (25 + y² – 6y)

36 = 4y

⇒ y = 9

The point is (0, 9)