document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1083554>Question 1083554</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The point p(3,-4) lies ..........the circle X^2+y^2+6x+8y=0<BR>\n" );
document.write( "a) inside<BR>\n" );
document.write( "b) outside<BR>\n" );
document.write( "c)on<BR>\n" );
document.write( "d)none </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #697563 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=697563\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=\"black\" face=\"times\" size=\"4\"><BR>\n" );
document.write( "Answer: <font color=red>Choice B) outside</font><BR>\n" );
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document.write( "Explanation:\r<BR>\n" );
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document.write( "The point (3,-4) is equal to (x,y). <BR>\n" );
document.write( "(x,y) = (3,-4)<BR>\n" );
document.write( "The x coordinate is x = 3<BR>\n" );
document.write( "The y coordinate is y = -4\r<BR>\n" );
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document.write( "Plug x = 3 and y = -4 into the the equation x^2+y^2+6x+8y=0 and simplify.\r<BR>\n" );
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document.write( "x^2+y^2+6x+8y=0<BR>\n" );
document.write( "(3)^2+(-4)^2+6(3)+8(-4)=0<BR>\n" );
document.write( "9+16+6(3)+8(-4)=0<BR>\n" );
document.write( "9+16+18-32=0<BR>\n" );
document.write( "25+18-32=0<BR>\n" );
document.write( "33-32=0<BR>\n" );
document.write( "1=0\r<BR>\n" );
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document.write( "The last equation (1 = 0) is false.<BR>\n" );
document.write( "So the point is NOT on the boundary of the circle.\r<BR>\n" );
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document.write( "The left side result is larger than 0, telling us that the point P is going to be on the <font color=red>outside of the circle</font>. \r<BR>\n" );
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document.write( "If we got a negative result on the left side, then P would be on the inside of the circle.\r<BR>\n" );
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document.write( "Visual Proof:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"https://i.imgur.com/GwY0Uoo.png\"><BR>\n" );
document.write( "(Image generated by <a  rel=nofollow HREF= \"https://www.geogebra.org/home?ggbLang=en\">GeoGebra</a> which is free graphing software)<BR>\n" );
document.write( "Note: The equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2By%5E2%2B6x%2B8y=0 ALIGN=MIDDLE  ALT=\"x%5E2%2By%5E2%2B6x%2B8y=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > is equivalent to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B3%29%5E2%2B%28y%2B4%29%5E2+=+25 ALIGN=MIDDLE  ALT=\"%28x%2B3%29%5E2%2B%28y%2B4%29%5E2+=+25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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