Question

find the coordinates of point which is on y - axis and which is equidistant from points (5,-2) and (3,4)​

Answer 1

Let P(0,y) be any point on y-axis.

Let A(5,−2) and B(−3,2). Then,

PA=PB

PA ^2

=PB ^2

(5−0) ^2

+(−2−y) ^2

=(−3−0) ^2

+(2−y) ^2

25+4+y ^2 +4y=9+4+y ^2 −4y

8y=−16

y=−2