I'm having some difficulty with this question. I can get to a certain point, and then the line equations cancel each other out. Can anyone help me out, please?

Many thanks.

Find the equations of the 2 circles which pass through the points (1, 2) & (-1, 4) & have a radius of length .

Q.

Attempt:Midpoint of (1, 2) & (-1, 4): (0, 3)

Slope: . Perpendicular slope: 1

Equation of bisector of (1, 2) & (-1, 4):

Define the equation of the circle as . Subbing in (1, 2) yields:...1, subbing in (-1, 4) yields:...2

Solving1&2as simultaneous equations yields: g - f = 3

From the bisector equation, because x -y + 3 = 0 contains centre c as (-g, -f), we can say -g + f = -3

Applying simultaneous equation approach to g - f = 3 & -g + f = -3: g/ f = 0...

Ans.:(From text book): &