document.write( "Question 394955: Find the equation of the circle (standard form) with center at (3,-4) and passing through (-1,-4). (show your soution) \n" ); document.write( "

Algebra.Com's Answer #280315 by Earlsdon(6294) $\"\"$ $\"About$

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Starting with the standard form for a circle of radius r and center at (h, k):
\n" ); document.write( " $\"%28x-h%29%5E2%2B%28y-k%29%5E2+=+r%5E2\"$
\n" ); document.write( "The center is given as (3, -4) so h = 3 and k = -4. Substitute.
\n" ); document.write( " $\"%28x-3%29%5E2%2B%28y%2B4%29%5E2+=+r%5E2\"$ Find $\"r%5E2\"$ by substituting the x- and y-coordinates of the given point and solving for r or use the distance formula to find the distance from the center (3, -4) to the point on the circle (-1, -4): $\"d+=+sqrt%28%28x%5B2%5D-x%5B1%5D%29%5E2%2B%28y%5B2%5D-y%5B1%5D%29%5E2%29\"$
\n" ); document.write( " $\"%28x-3%29%5E2%2B%28y%2B4%29%5E2+=+r%5E2\"$ Substitute x = -1 and y = -4.
\n" ); document.write( " $\"%28-1-3%29%5E2%2B%28-4%2B4%29%5E2+=+r%5E2\"$ Evaluate.
\n" ); document.write( " $\"%28-4%29%5E2+=+r%5E2\"$
\n" ); document.write( " $\"16+=+r%5E2\"$
\n" ); document.write( "Final equation is:
\n" ); document.write( " $\"%28x-3%29%5E2%2B%28y%2B4%29%5E2+=+16\"$ \n" ); document.write( "

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