document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=202800>Question 202800</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 3x^2+3y^2-24x-12y-15=0 Graph the circle using (h,k) and R find the intercepts if any </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #152971 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=152971\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2%2B3y%5E2-24x-12y-15+=+0 ALIGN=MIDDLE  ALT=\"3x%5E2%2B3y%5E2-24x-12y-15+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 3.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2By%5E3-8x-4y+-5+=+0 ALIGN=MIDDLE  ALT=\"x%5E2%2By%5E3-8x-4y+-5+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Group the x- and y-terms as shown:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2-8x%29%2B%28y%5E2-4y%29-5+=+0 ALIGN=MIDDLE  ALT=\"%28x%5E2-8x%29%2B%28y%5E2-4y%29-5+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add 5 to both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2-8x%29%2B%28y%5E2-4y%29+=+5 ALIGN=MIDDLE  ALT=\"%28x%5E2-8x%29%2B%28y%5E2-4y%29+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Complete the square in both the x-terms and the y-terms.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2-8x%2B16%29%2B%28y%5E2-4y%2B4%29+=+5%2B16%2B4 ALIGN=MIDDLE  ALT=\"%28x%5E2-8x%2B16%29%2B%28y%5E2-4y%2B4%29+=+5%2B16%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor the left groups ans simplify the right side.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-4%29%5E2%2B%28y-2%29%5E2+=+25 ALIGN=MIDDLE  ALT=\"%28x-4%29%5E2%2B%28y-2%29%5E2+=+25\"   DISABLED_style= \"max-width:90%; height:auto;\" > Compare with the standard form for a circle with center at (h, k) and radius r.<BR>\n" );
document.write( "<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( "The center is at (4, 2) and the radius is 5.<BR>\n" );
document.write( "To graph this circle, we will have to solve this equation for y and the graph each of the two solutions separately.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-4%29%5E2%2B%28y-2%29%5E2+=+25 ALIGN=MIDDLE  ALT=\"%28x-4%29%5E2%2B%28y-2%29%5E2+=+25\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-4%29%5E2 ALIGN=MIDDLE  ALT=\"%28x-4%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y-2%29%5E2+=+-%28x-4%29%5E2%2B25 ALIGN=MIDDLE  ALT=\"%28y-2%29%5E2+=+-%28x-4%29%5E2%2B25\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify the right side.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y-2%29%5E2+=+-%28x%5E2-8x%2B16%29%2B25 ALIGN=MIDDLE  ALT=\"%28y-2%29%5E2+=+-%28x%5E2-8x%2B16%29%2B25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y-2%29%5E2+=+-x%5E2%2B8x-16%2B25 ALIGN=MIDDLE  ALT=\"%28y-2%29%5E2+=+-x%5E2%2B8x-16%2B25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y-2%29%5E2+=+-x%5E2%2B8x%2B9 ALIGN=MIDDLE  ALT=\"%28y-2%29%5E2+=+-x%5E2%2B8x%2B9\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root of both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-2+=+sqrt%28-x%5E2%2B8x%2B9%29 ALIGN=MIDDLE  ALT=\"y-2+=+sqrt%28-x%5E2%2B8x%2B9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > The right side should have a + or - sign in front. Add 2 to both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+2%2B-sqrt%28-x%5E2%2B8x%2B9%29 ALIGN=MIDDLE  ALT=\"y+=+2%2B-sqrt%28-x%5E2%2B8x%2B9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now graph both of these solutions.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-2%2C10%2C-4%2C8%2C2%2Bsqrt%28-x%5E2%2B8x%2B9%29%2C2-sqrt%28-x%5E2%2B8x%2B9%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The y-intercepts are: (0, 5) and (0, -1)<BR>\n" );
document.write( "The x-intercepts are: (8.58, 0) and (-0.58, 0) </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );