document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=896289>Question 896289</A>: <I><SPAN STYLE=\"word-break: break-all;\"> what will be the length of the chord of the circle x^2-2x+1+y^2+2y+1=25 , passing through the point (1,-1)? can you please let me know the formula used here as well?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #543372 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=543372\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the formula for a circle that you need is:\r<BR>\n" );
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document.write( "(x-h)^2 + (y-k)^2 = r^2\r<BR>\n" );
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document.write( "your equation can be converted into this form easily since it's pretty much set up to allow you to do without a lot of manipulation.\r<BR>\n" );
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document.write( "your equation is:\r<BR>\n" );
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document.write( "x^2-2x+1+y^2+2y+1=25\r<BR>\n" );
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document.write( "this can be separated into 2 parts.\r<BR>\n" );
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document.write( "(x^2 - 2x + 1) + (y^2 + 2y + 1) = 25\r<BR>\n" );
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document.write( "the first part can be factored into (x-1)^2.<BR>\n" );
document.write( "the second part can be factored into (y+1)^2.\r<BR>\n" );
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document.write( "your equation becomes:\r<BR>\n" );
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document.write( "(x-1)^2 + (y+1)^2 = 25\r<BR>\n" );
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document.write( "now it's in  the form of (x-h)^2 + (y-k)^2 = r^2\r<BR>\n" );
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document.write( "h is the x-coordinate of the center of the circle.<BR>\n" );
document.write( "k is the y-coordinate of the center of the circle.<BR>\n" );
document.write( "r is the radius of the circle.\r<BR>\n" );
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document.write( "this means that h is equal to 1 because x-h becomes x-1 when h is equal to 1.\r<BR>\n" );
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document.write( "this means that k is equal to -1 because y-k becomes y-(-1) = y+1 when k is equal to -1.\r<BR>\n" );
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document.write( "the chord is passing through the point (1,-1) which is the center of the circle.\r<BR>\n" );
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document.write( "if the chord passes through the center of the circle, then the chord is a diameter of the circle.\r<BR>\n" );
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document.write( "the radius of the circle is 5 since r^2 = 25.\r<BR>\n" );
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document.write( "the diameter is equal to 2 * the radius, so the diameter must be equal to 10.\r<BR>\n" );
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document.write( "that's your answer.\r<BR>\n" );
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document.write( "the chord that passes through the point (1,-1) is equal to 10 units in length.<BR>\n" );
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