Can't seem to figure this out – the question is:
There are exactly two circles of radius $r = \sqrt{5}$ through the points $(6,3)$ and $(7,2)$. Find the equations of both circles.
I was thinking that I would find the equation of the line passing through these two points which would give me a chord on the circle. I could then find a line perpendicular to this by taking the negative reciprocal. This perpendicular bisector of the chord would pass through the center of the circle (which I'm assuming I need to find).
Am I making this more complicated than it actually is…? I don't know where to go from here
Best Answer
Alternately, note that $(h,k)$ will be the center of such a circle if and only if $$(6-h)^2+(3-k)^2=5$$ and $$(7-h)^2+(2-k)^2=5.$$ Solving this system for $h$ and $k$ (there will be two possible solutions) will give you the desired circles.