SOLUTION: Write the equation of the circle if the center is on the x-axis and it is passing through (0,0) and (2,4)

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Question 1124882: Write the equation of the circle if the center is on the x-axis and it is passing through (0,0) and (2,4)
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!
The general equation of a circle with center at (h,k) and radius r is:
+%28x-h%29%5E2+%2B+%28y-k%29%5E2+=+r%5E2+

What is known:
+k+=+0+
and
+r%5E2+=+h%5E2+=+%282-h%29%5E2+%2B+%284%29%5E2+

Solving the bottom equation for h:
+h%5E2+=+%284-4h%2Bh%5E2%29%2B16+
+++0+=+20-4h+
++4h+=+20+
++h+=+5+

Center is at (5,0), r=5, so the equation is:
++highlight%28+%28x-5%29%5E2+%2B+y%5E2+=+5%5E2+%29+
——
Check: (2,4) should solve the equation:
+%282-5%29%5E2+%2B+%284%29%5E2+=+9+%2B+16+=+25+=+5%5E2+ (ok)

(0,0) should also solve the equation:
++%28-5%29%5E2+%2B+0%5E2+=+25+ (ok)