(Q24)Find a point on Y-axis which is equidistant from both the points A(6,5) and B(-4,3).

Answer

We know that a point on the Y-axis is of the form (0,y) so, let the point P(0,y) be equidistant from A and B. Then

PA=√(( - 0)2 + ( - y)2)

PB=√((- - 0)2 + ( - y)2)

PA2=PB2

( - 0)2+( -y)2= (- - 0)2+( - y)2

+25+y2-y=+9+y2-y

4y=

y=

So the required point is (0,)

So (0,) is equidistant from(6,5) and (4,3).