SOLUTION: Write the equation of a circle with the following characteristics: Diameter of 6 Point (5, 3) lies on circle Point (2, 0) lies on the circle

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Question 1045169: Write the equation of a circle with the following characteristics: Diameter of 6 Point (5, 3) lies on circle Point (2, 0) lies on the circle
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
What line contains the two points? What line is perpendicular and contains their midpoint? The center of the circle is on the intersection of these two lines.


%283-0%29%2F%285-2%29
3%2F3
1
You want line with slope -1 containing system%28x=%285%2B2%29%2F2=3%2F2%2C+y=%283%2B0%29%2F2=3%2F2%29, or the point ( 3/2, 3/2 ).
Line containing the center is y-3%2F2=-1%28x-3%2F2%29
y-3%2F2=-x%2B3%2F2
y=-x%2B6%2F2
highlight_green%28y=-x%2B3%29


Diameter of 6 means RADIUS of 3.
Put this description in the form of the DISTANCE FORMULA:
The distance from (x, -x+3 ) to (5,3) must be 3;
and distance from (x, -x+3) to (2,0) must also be 3.