document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=544659>Question 544659</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Name a point that is sqrt(2)away from (-1,5).\r<BR>\n" );
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document.write( "Name a point that is between 50 and 60 units away from (7,-2) and state the distance between from the two points.\r<BR>\n" );
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document.write( "Could you show me how to work them out? Please?<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 #355189 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=355189\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "All points a given distance from a given point is a circle where the given point is the center.  The equation of a circle with center at the point <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \left(h,k\right)\"> and radius <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large r\"> is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large (x\ -\ h)^2\ (y\ -\ k)^2\ =\ r^2\">\r<BR>\n" );
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document.write( "So any point where the coordinates of the ordered pair identifying that point satisfy\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \left(x\ -\ (-1)\right)^2\ +\ \left(y\ -\ 5\right)^2\ =\ 2\">\r<BR>\n" );
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document.write( "is, by definition of a circle, the radius, i.e. <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \sqrt{2}\">, distant from the given point (-1, 5).\r<BR>\n" );
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document.write( "There are two ways to proceed.  You can pick any value you like for either <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\"> in the interval <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large -1\ -\ \sqrt{2}\ \leq\ x\ \leq\ -1\ +\ \sqrt{2}\"> or <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y\"> in the interval <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 5\ -\ \sqrt{2}\ \leq\ y\ \leq\ 5\ +\ \sqrt{2}\">, substitute that value, and then solve for the value of the other variable, giving you an ordered pair that is on the circle and the proper distance from the given point.\r<BR>\n" );
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document.write( "Or you can do it the easy way:  Replace the coordinate -1 in the given point with either <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large -1\ +\ \sqrt{2}\"> or <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large -1\ -\ \sqrt{2}\"> OR replace the coordinate 5 in the given point with either <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 5\ +\ \sqrt{2}\"> or <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 5\ -\ \sqrt{2}\">. \r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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