document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=298099>Question 298099</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is the equation in standard form for the circle: x^2+y^2-4x+8y+4=0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #214534 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=214534\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Rewrite in standard form:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2By%5E2-4x%2B8y%2B4+=+0 ALIGN=MIDDLE  ALT=\"x%5E2%2By%5E2-4x%2B8y%2B4+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Group the x-terms and the y-terms as shown:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2-4x%29%2B%28y%5E2%2B8y%29%2B4+=+0 ALIGN=MIDDLE  ALT=\"%28x%5E2-4x%29%2B%28y%5E2%2B8y%29%2B4+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 4 from both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-4x%29%2B%28y%5E2%2B8y%29+=+-4 ALIGN=MIDDLE  ALT=\"x%5E2-4x%29%2B%28y%5E2%2B8y%29+=+-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now complete the square in x and y by adding the square of half the x-term coefficient and the square of half the y-term coefficient to both sides of the equation.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2-4x%2Bhighlight%28%28-4%2F2%29%5E2%29%29%2B%28y%5E2%2B8y%2Bhighlight_green%28%288%2F2%29%5E2%29%29+=+-4%2Bhighlight%28%28-4%2F2%29%5E2%29%2Bhighlight_green%28%288%2F2%29%5E2%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify both sides of the equation.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2-4x%2B4%29%2B%28y%5E2%2B8y%2B16%29+=+-4%2B4%2B16 ALIGN=MIDDLE  ALT=\"%28x%5E2-4x%2B4%29%2B%28y%5E2%2B8y%2B16%29+=+-4%2B4%2B16\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now factor the left side and simplify the right side.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-2%29%5E2%2B%28y%2B4%29%5E2+=+16 ALIGN=MIDDLE  ALT=\"%28x-2%29%5E2%2B%28y%2B4%29%5E2+=+16\"   DISABLED_style= \"max-width:90%; height:auto;\" > Finally...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28%28x-2%29%5E2%2B%28y%2B4%29%5E2+=+4%5E2%29 ALIGN=MIDDLE  ALT=\"highlight%28%28x-2%29%5E2%2B%28y%2B4%29%5E2+=+4%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Compare with standard form...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2Bh%29%5E2%2B%28y%2Bk%29%5E2+=+r%5E2 ALIGN=MIDDLE  ALT=\"%28x%2Bh%29%5E2%2B%28y%2Bk%29%5E2+=+r%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and you can see that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h+=+-2 ALIGN=MIDDLE  ALT=\"h+=+-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k+=+4 ALIGN=MIDDLE  ALT=\"k+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+4 ALIGN=MIDDLE  ALT=\"r+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" > and this represents a circle with center at (-2, 4) and radius of 4. </SPAN>\n" );
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