document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=256816>Question 256816</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A hyperbolic mirror (used in some telescopes) has property that a light ray directed at a focus will be reflected to the other focus. The focus of a hyperbolic mirror can be represented on a rectangular coordinate system by coordinates (24,0). Find the vertex of the mirror if the Mount at the the top edge of the mirror has coordinates (24,24). Sketch the focus, vertex, and part of the hyperbola to represent the mirror. Can you explain this? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #188854 by </B><A HREF=/tutors/aboutme.mpl?userid=drk><B>drk(1908)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=drk><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=188854\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Vertex = (0,0)<BR>\n" );
document.write( "Focus = (24,0)<BR>\n" );
document.write( "point on parabola = (24,24)<BR>\n" );
document.write( "The  general equation is<BR>\n" );
document.write( "(i) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+a%28x-h%29%5E2+%2B+k ALIGN=MIDDLE  ALT=\"y+=+a%28x-h%29%5E2+%2B+k\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or <BR>\n" );
document.write( "(ii) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%281%2F4p%29%28x-h%29%5E2+%2B+k ALIGN=MIDDLE  ALT=\"y+=+%281%2F4p%29%28x-h%29%5E2+%2B+k\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "From the given information, we get<BR>\n" );
document.write( "(iii) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+a%28x-+0%29%5E2+%2B+0 ALIGN=MIDDLE  ALT=\"y+=+a%28x-+0%29%5E2+%2B+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or<BR>\n" );
document.write( "(iv) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+ax%5E2 ALIGN=MIDDLE  ALT=\"y+=+ax%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now we have the coordinate 24,24, so (iv) becomes<BR>\n" );
document.write( "(v) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24+=+a%2824%29%5E2 ALIGN=MIDDLE  ALT=\"24+=+a%2824%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "solving for a, we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+1%2F24 ALIGN=MIDDLE  ALT=\"a+=+1%2F24\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So, our answer is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%281%2F24%29x%5E2 ALIGN=MIDDLE  ALT=\"y+=+%281%2F24%29x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );