SOLUTION: Determine the equations of the equation of the circle defined by the given conditions a) the circle passes through ( 2,2) and( 5,3) , center is on the line y = x+2 Can you plea

Algebra ->  Circles -> SOLUTION: Determine the equations of the equation of the circle defined by the given conditions a) the circle passes through ( 2,2) and( 5,3) , center is on the line y = x+2 Can you plea      Log On


   

Question 800663: Determine the equations of the equation of the circle defined by the given conditions
a) the circle passes through ( 2,2) and( 5,3) , center is on the line y = x+2
Can you please help me thanks so much in advance:)
Answer by josgarithmetic(39625) About Me  (Show Source):
You can put this solution on YOUR website!
Using the given line, the center of this circle must be on some general point (x,x+2).

One radius is sqrt%28%28x-2%29%5E2%2B%28x%2B2-2%29%5E2%29 and another radius is sqrt%28%28x-5%29%5E2%2B%28x%2B2-3%29%5E2%29.
Simplifying somewhat, these radius expressions are sqrt%28%28x-2%29%5E2%2B%28x%29%5E2%29 and sqrt%28%28x-5%29%5E2%2B%28x-1%29%5E2%29


.
2x%5E2-4x%2B4=2x%5E2-12x%2B26
-4x%2B4=-12x%2B26
8x%2B4=26
8x=22
x=22%2F8
highlight%28x=11%2F4%29, this is much of the way to the answer, but solution is not yet complete. You can finish this....?
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(Use line or general center point to find the actual center. Compute the actual radius length. Put information into standard form equation for a circle).