document.write( "Question 16395: I need to know how to find the radius and center of x2 - 2x + y2 – 16y = – 1. \n" ); document.write( "

Algebra.Com's Answer #8042 by Earlsdon(6294) $\"\"$ $\"About$

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You need to get your equation into the standard form for a circle whose centre is at (h, k) and whose radius is r.\r
\n" ); document.write( "\n" ); document.write( " $\"%28x+-+h%29%5E2+%2B+%28y+-+k%29%5E2+=+r%5E2\"$ \r
\n" ); document.write( "\n" ); document.write( "You can accomplish this by completing the squares in the x-terms and in the y-terms, then factoring the resulting trinomial in x and factoring the resulting trinomial in y. Start by grouping the x-terms and grouping the y-terms.
\n" ); document.write( " $\"%28x%5E2+-+2x%29+%2B+%28y%5E2+-+16y%29+=+-1\"$ Complete the sqauare in the x-terms by adding the square of half the coefficient of x. Similarly for the y-terms. Don't forget to add these to both sides of the equation.\r
\n" ); document.write( "\n" ); document.write( " $\"%28x%5E2+-+2x+%2B+1%29+%2B+%28y%5E2+-+16y+%2B+64%29+=+-1+%2B+1+%2B+64\"$ Simplify and factor the x-trinomial and the y-trinomial.
\n" ); document.write( " $\"%28x+-+1%29%5E2+%2B+%28y+-+8%29%5E2+=+64\"$ Compare this with the standard form:
\n" ); document.write( " $\"%28x+-+h%29%5E2+%2B+%28y+-+k%29%5E2+=+r%5E2\"$ \r
\n" ); document.write( "\n" ); document.write( "The centre of the circle is at (1, 8) and its radius is $\"sqrt%2864%29+=+8\"$
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