if I am given two points on the diameter of a circle, how do I come up with a standard form equation for that circle? I was given (-2,4) and (4,2). I think the center of the circle is at (1,3) but I may be wrong.

Question

if I am given two points on the diameter of a circle, how do I come up with a standard form equation for that circle?  I was given (-2,4) and (4,2).  I think the center of the circle is at (1,3) but I may be wrong.

anonymous · Answer

What formula did you use to find the center?

anonymous · Answer

find the midpoint (that's the center), then find the distance between the two and divide by two to get the radius

anonymous · Answer

Yep, I agree

anonymous · Answer

then plug that information into the equation of a circle formula

anonymous · Answer

I did not use a formula, I just drew it on a piece of graph paper and counted units from point to point. Halfway was a 1,3... yeah I know that is not right, but I have no clue what the heck I am doing here!

anonymous · Answer

$$(x-h)^{2}+(y-k)^{2}=r ^{2}$$(h,k) is center, r is radius, half the distance between two given points.

anonymous · Answer

ok, I am confused here... how do I determine the center??

anonymous · Answer

There are several ways, one way is to find the midway point of the two given points. The midpoint formula$$((x _{1}+x _{2})/2, (y _{1}+y _{2})/2) $$

anonymous · Answer

ahhhhh.... that I can work with, thanks!

anonymous · Answer

sweet, my center point was right... but it was just dumb luck I am sure... LOL

anonymous · Answer

Sure you can count the graph, but it is not a very efficient method. For example, in a test it may not be given on a graph and may take too much time to make a graph.