document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=145089>Question 145089</A>: <I><SPAN STYLE=\"word-break: break-all;\"> could anyone help me with these two questions?\r<BR>\n" );
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document.write( "1. Is the graph of a circle a graph of a function? (Yes or no)\r<BR>\n" );
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document.write( "2. Find the center and the radius of the circle represented by the equation<BR>\n" );
document.write( "x2 + y2 + 10x – 4y – 7 = 0<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #105772 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=105772\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1) The answer is NO! You can check this by using the \"vertical line test\" in which you draw a vertical line through the circle on the graph containing the circle. <BR>\n" );
document.write( "If the vertical line passes through the graph (circle) only once, then the graph is a function. In the case of a circle, the vertical line would pass through the graph (circle) twice, so the equation represented by the graph is not a function.<BR>\n" );
document.write( "2) Find the center and the radius of the circle represented by the equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2By%5E2%2B10x-4y-7+=+0 ALIGN=MIDDLE  ALT=\"x%5E2%2By%5E2%2B10x-4y-7+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The goal is to transform this equation into the standard form of the equation for a circle with center at (h, k) and radius r, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-h%29%5E2%2B%28y-k%29%5E2+=+r%5E2 ALIGN=MIDDLE  ALT=\"%28x-h%29%5E2%2B%28y-k%29%5E2+=+r%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  First, add 7 to both sides of the equation.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2By%5E2%2B10x-4y+=+7 ALIGN=MIDDLE  ALT=\"x%5E2%2By%5E2%2B10x-4y+=+7\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now group the x-terms together and the y-terms together.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2%2B10x%29%2B%28y%5E2-4y%29+=+7 ALIGN=MIDDLE  ALT=\"%28x%5E2%2B10x%29%2B%28y%5E2-4y%29+=+7\"   DISABLED_style= \"max-width:90%; height:auto;\" > The next step is to \"complete the square\" in both the x-terms and the y-terms.  You do this by adding the square of half the x-coefficient: (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2810%2F2%29%5E2+=+25 ALIGN=MIDDLE  ALT=\"%2810%2F2%29%5E2+=+25\"   DISABLED_style= \"max-width:90%; height:auto;\" >) and likewise for the y-coefficient (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-4%2F2%29%5E2+=+4 ALIGN=MIDDLE  ALT=\"%28-4%2F2%29%5E2+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" >) to both sides of the equation.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2%2B10x%2B25%29%2B%28y%5E2-4y%2B4%29+=+7%2B25%2B4 ALIGN=MIDDLE  ALT=\"%28x%5E2%2B10x%2B25%29%2B%28y%5E2-4y%2B4%29+=+7%2B25%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now factor the x- and y-groups and simplify.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B5%29%5E2%2B%28y-2%29%5E2+=+36 ALIGN=MIDDLE  ALT=\"%28x%2B5%29%5E2%2B%28y-2%29%5E2+=+36\"   DISABLED_style= \"max-width:90%; height:auto;\" > Compare this with the standard form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-h%29%5E2%2B%28y-k%29%5E2+=+r%5E2 ALIGN=MIDDLE  ALT=\"%28x-h%29%5E2%2B%28y-k%29%5E2+=+r%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "You can see that h = -5, k = 2, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5E2+=+36 ALIGN=MIDDLE  ALT=\"r%5E2+=+36\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So, the center is at (h,k) = (-5,2) and the radius, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+sqrt%2836%29 ALIGN=MIDDLE  ALT=\"r+=+sqrt%2836%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 6.<BR>\n" );
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