document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1165093>Question 1165093</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A seismological station is located at (0 ,3), 3 km away from a straight shoreline<BR>\n" );
document.write( "where the x-axis runs through. The epicenter of an earthquake was determined to<BR>\n" );
document.write( "be 6 km away from the station.\r<BR>\n" );
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document.write( "(a) Find the equation of the curve that contains the possible location of the<BR>\n" );
document.write( "epicenter.\r<BR>\n" );
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document.write( "(b) If furthermore, the epicenter was determined to be 2 km away from the shore,<BR>\n" );
document.write( "find its possible coordinates (rounded off to two decimal places).<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 #853132 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20854)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=853132\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "Here we have a circle, so the equation will be in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-x%5B0%5D%29%5E2+%2B+%28y-y%5B0%5D%29%5E2+=+r%5E2+ ALIGN=MIDDLE  ALT=\"%28x-x%5B0%5D%29%5E2+%2B+%28y-y%5B0%5D%29%5E2+=+r%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >where (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B0%5D ALIGN=MIDDLE  ALT=\"x%5B0%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B0%5D ALIGN=MIDDLE  ALT=\"y%5B0%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >) is the center of the circle.\r<BR>\n" );
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document.write( "For part a, the radius <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r ALIGN=MIDDLE  ALT=\"r\"   DISABLED_style= \"max-width:90%; height:auto;\" > of the circle representing the possible locations of the epicenter is the distance from the station to the epicenter, which is<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+r=6 ALIGN=MIDDLE  ALT=\"+r=6\"   DISABLED_style= \"max-width:90%; height:auto;\" > km.\r<BR>\n" );
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document.write( "Since given that the station is at (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" >), the center of the circle is at that point, and the equation becomes\r<BR>\n" );
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document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-0%29%5E2+%2B+%28y-3%29%5E2+=+6%5E2 ALIGN=MIDDLE  ALT=\"%28x-0%29%5E2+%2B+%28y-3%29%5E2+=+6%5E2\"   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=x%5E2+%2B+%28y-3%29%5E2+=+36 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+%28y-3%29%5E2+=+36\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "This is the equation of the curve that contains the possible location of the epicenter.\r<BR>\n" );
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document.write( "For part b, when the epicenter is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2km ALIGN=MIDDLE  ALT=\"2km\"   DISABLED_style= \"max-width:90%; height:auto;\" > away from the shore, we need to find the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >-coordinates where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+2 ALIGN=MIDDLE  ALT=\"y+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+2 ALIGN=MIDDLE  ALT=\"y+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > into the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+%28y-3%29%5E2+=+36 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+%28y-3%29%5E2+=+36\"   DISABLED_style= \"max-width:90%; height:auto;\" >:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+%282-3%29%5E2+=+36 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+%282-3%29%5E2+=+36\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+%28-1%29%5E2+=+36 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+%28-1%29%5E2+=+36\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+1+=+36 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+1+=+36\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2++=+35 ALIGN=MIDDLE  ALT=\"x%5E2++=+35\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=sqrt%2835%29 ALIGN=MIDDLE  ALT=\"x=sqrt%2835%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "solutions: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=5.92 ALIGN=MIDDLE  ALT=\"x=5.92\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-5.92 ALIGN=MIDDLE  ALT=\"x=-5.92\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so, the coordinates of the epicenter are (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5.92 ALIGN=MIDDLE  ALT=\"5.92\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" >) or (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5.92 ALIGN=MIDDLE  ALT=\"-5.92\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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