Question

find the point on Y-axis ehich is equidistant from points A {8,5} and B{4,3}

Answer 1

Let P is point on y-axis with coordinates (0,y)
A/Q,
PA=PB
PA^2 = PB^2
(0-8)^2 + (y-5)^2 = (0-4)^2 + (y-3)^2 {by distance formula}
64+y^2+25-10y = 16+y^2+ 9-6y
y^2-10y+89 = y^2-6y+25
y^2-y^2-10y+6y+89-25 = 0
-4y+64 = 0
4y = 64
y = 16
Coordinates of P = (0,16)