Hint: The distance between the centre and the points it passes through is equal to the radius.
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): &