Question

find the coordinates of the point c that lies on the y-axis and is equidistant from a(2,2) and b(1,5) help please

Answer 1

a point on the \(y\) axis looks like \((0,y)\) the square of the distnace between that point and \((2,2)\) is \(2^2+(y-2)^2=y^2-4y+8\)
the square of the distance between \((0,y)\) and \((1,5)\) is
\[1^2+(y-5)^2=y^2-10y+26\]
set them equal, solve for \(y\)