document.write( "Question 510115: I'm supposed to find the standard form of the equation of a circle. The question is center at the origin containing the point: (-2,3). I have no idea where to begin. I've been working on this problem for about 2 hours. That answer in the back of the book is x^2+y^2=13. \n" ); document.write( "

Algebra.Com's Answer #341724 by Earlsdon(6294) $\"\"$ $\"About$

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Start with the basic equation of a circle with center at (h,k) and radius, r.
\n" ); document.write( " $\"%28x-h%29%5E2%2B%28y-k%29%5E2+=+r%5E2\"$ The center is at the origin, so (h,k) = (0,0). Substitute this.
\n" ); document.write( " $\"%28x-0%29%5E2%2B%28y-0%29%5E2+=+r%5E2\"$ which can be simplified to...
\n" ); document.write( " $\"x%5E2%2By%5E2+=+r%5E2\"$ Now to find $\"r%5E2\"$ you use the distance formula: $\"d%5E2+=+%28x%5B2%5D-x%5B1%5D%29%5E2%2B%28y%5B2%5D-y%5B1%5D%29%5E2\"$ in which you'll find the distance between the circle's center (0,0) and the point contained on the cirle (-2,3).
\n" ); document.write( " $\"d%5E2+=+%28-2-0%29%5E2%2B%283-0%29%5E2\"$
\n" ); document.write( " $\"d%5E2+=+4%2B9\"$
\n" ); document.write( " $\"d%5E2+=+13\"$ but this is just $\"r%5E2\"$ so you substitute...
\n" ); document.write( " $\"x%5E2%2By%5E2+=+13\"$ \n" ); document.write( "

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