SOLUTION: How do you find the center of a circle with the intercepts of (1,2) and (4,2) and then it must be in standard form and I know equation for that. Thanks.

Question 242062: How do you find the center of a circle with the intercepts of (1,2) and (4,2) and then it must be in standard form and I know equation for that.
Thanks.
Found 2 solutions by Alan3354, solver91311:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
How do you find the center of a circle with the intercepts of (1,2) and (4,2) and then it must be in standard form and I know equation for that.
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3 points are needed to define a circle, or one point and the center.
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With only those 2 points and no other info, the center of the circle will be on the line x = 2.5.
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Why are the 2 points called "intercepts?"
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

No can do, pal. In the first place, (1,2) and (4,2) are not intercepts. Intercepts are where a graph intersects one or the other of the axes, therefore at least one of the coordinates in an intercept must be zero. In the second place, even if you did give proper intercepts, you cannot determine a circle with only 2 points unless one of them is the center. Clearly, since you want to know the center, neither of your given points is the center of this circle. You need to specify at least three points on a circle to be able to uniquely define the circle.

John

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