SOLUTION: Please help me solve this problem: Find the equation of a circle that passes through (2,2) and tangent to the lines x=1 and x=6. Thank you in advance!

Algebra ->  Circles -> SOLUTION: Please help me solve this problem: Find the equation of a circle that passes through (2,2) and tangent to the lines x=1 and x=6. Thank you in advance!      Log On


   

Question 979454: Please help me solve this problem: Find the equation of a circle that passes through (2,2) and tangent to the lines x=1 and x=6. Thank you in advance!
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Find the equation of a circle that passes through (2,2) and tangent to the lines x=1 and x=6.
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The center has to be on the line midway between x=1 and x=6, which is
x = 3.5
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The radius is the distance from x=3.5 to the tangent lines, r = 2.5
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The center is on the line x = 3.5 and is 2.5 units from the point (2,2).
The circle with its center at (2,2) and r=2.5 is
%28x-2%29%5E2+%2B+%28y-2%29%5E2+=+2.5%5E2
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Find the intersection of %28x-2%29%5E2+%2B+%28y-2%29%5E2+=+2.5%5E2 and x=3.5
Sub 3.5 for x and solve for y:
%283.5-2%29%5E2+%2B+%28y-2%29%5E2+=+2.5%5E2
2.25+%2B+y%5E2+-+4y+%2B+4+=+6.25
y%5E2+-+4y+=+0
y = 0, y = 4
The 2 centers are (3.5,0) and (3.5,4)
Can you finish it?