
Equation of a Circle
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.
Q. Find the equations of the 2 circles which pass through the points (1, 2) & (1, 4) & have a radius of length .
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
Solving 1 & 2 as 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): &

Re: Equation of a Circle
Hint: The distance between the centre and the points it passes through is equal to the radius.

Re: Equation of a Circle
Am I on the right track with
For (1, 2):
For (1, 4):
Thus

Re: Equation of a Circle
Yes you are on the right track

Re: Equation of a Circle
Ok, I have it now. Thank you very much.

1 Attachment(s)
Re: Equation of a Circle
Here is the solution
Attachment 28374