document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1024962>Question 1024962</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The point (a,b) is 5 units away from the point (6,3), and (a,b) lies on the line 5x - 4y = -14. What is the largest possible value of a? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #640362 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=640362\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> There must be a less painful way to do this.<BR>\n" );
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document.write( "The distance from (a,b) to (6,3) is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%28a-6%29%5E2%2B%28b-3%29%5E2%29=5 ALIGN=MIDDLE  ALT=\"sqrt%28%28a-6%29%5E2%2B%28b-3%29%5E2%29=5\"   DISABLED_style= \"max-width:90%; height:auto;\" > , so<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a-6%29%5E2%2B%28b-3%29%5E2=25 ALIGN=MIDDLE  ALT=\"%28a-6%29%5E2%2B%28b-3%29%5E2=25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5a-4b=14 ALIGN=MIDDLE  ALT=\"5a-4b=14\"   DISABLED_style= \"max-width:90%; height:auto;\" > because point (a,b) ies on the line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x+-+4y+=+-14 ALIGN=MIDDLE  ALT=\"5x+-+4y+=+-14\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5a-4b=14 ALIGN=MIDDLE  ALT=\"5a-4b=14\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=%285%2F4%29a%2B7%2F2 ALIGN=MIDDLE  ALT=\"b=%285%2F4%29a%2B7%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b-3=%285%2F4%29a%2B1%2F2 ALIGN=MIDDLE  ALT=\"b-3=%285%2F4%29a%2B1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28b-3%29%5E2=%2825%2F16%29a%5E2%2B%285%2F4%29a%2B1%2F4 ALIGN=MIDDLE  ALT=\"%28b-3%29%5E2=%2825%2F16%29a%5E2%2B%285%2F4%29a%2B1%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Substituting that expression in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a-6%29%5E2%2B%28b-3%29%5E2=25 ALIGN=MIDDLE  ALT=\"%28a-6%29%5E2%2B%28b-3%29%5E2=25\"   DISABLED_style= \"max-width:90%; height:auto;\" > we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a-6%29%5E2%2B%2825%2F16%29a%5E2%2B%285%2F4%29a%2B1%2F4=25 ALIGN=MIDDLE  ALT=\"%28a-6%29%5E2%2B%2825%2F16%29a%5E2%2B%285%2F4%29a%2B1%2F4=25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2-12a%2B36%2B%2825%2F16%29a%5E2%2B%285%2F4%29a%2B1%2F4=25 ALIGN=MIDDLE  ALT=\"a%5E2-12a%2B36%2B%2825%2F16%29a%5E2%2B%285%2F4%29a%2B1%2F4=25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Multiplying both sides of the equal sign times <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16 ALIGN=MIDDLE  ALT=\"16\"   DISABLED_style= \"max-width:90%; height:auto;\" > , we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16a%5E2-192a%2B576%2B25a%5E2%2B20a%2B4=400 ALIGN=MIDDLE  ALT=\"16a%5E2-192a%2B576%2B25a%5E2%2B20a%2B4=400\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=41a%5E2-172a%2B180=0 ALIGN=MIDDLE  ALT=\"41a%5E2-172a%2B180=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Applying the quadratic formula, we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+%28-%28-172%29+%2B-+sqrt%28%28-172%29%5E2-4%2A41%2A180+%29%29%2F%282%2A41%29+ ALIGN=MIDDLE  ALT=\"a+=+%28-%28-172%29+%2B-+sqrt%28%28-172%29%5E2-4%2A41%2A180+%29%29%2F%282%2A41%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+%28172+%2B-+sqrt%2829584-29520%29%29%2F82 ALIGN=MIDDLE  ALT=\"a+=+%28172+%2B-+sqrt%2829584-29520%29%29%2F82\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+%28172+%2B-+sqrt%2864%29%29%2F82 ALIGN=MIDDLE  ALT=\"a+=+%28172+%2B-+sqrt%2864%29%29%2F82\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+%28172+%2B-+8%29%2F82 ALIGN=MIDDLE  ALT=\"a+=+%28172+%2B-+8%29%2F82\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28a=%28172-8%29%2F82=164%2F82=2%2C%22or%22%2Ca=%28172%2B8%29%2F82=180%2F82=highlight%2890%2F41%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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