document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=246720>Question 246720</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have a math question with two parts.  I am trying to work through the problem but am so confused.  The question is as follows:\r<BR>\n" );
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document.write( "Part 1)  P is the parabola with focus (3,1) and directrix x=7.  I have placed on the graph the focus (3,1) and the directrix x = 7 and have come up with a vertex of (5,1).  The equation I am using is x-h=a(y-k)^2.  But I am confused as to what the true equation looks like.\r<BR>\n" );
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document.write( "Part 2)  H is the hyperbola with a center at (1,1), an x-intercept at (2,0) and one vertex at (5/4,1).  I am completely lost with this one.\r<BR>\n" );
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document.write( "Any help would be greatly appreciated.  \r<BR>\n" );
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document.write( "Lori </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #180288 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=180288\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The question is as follows: <BR>\n" );
document.write( "Part A) P is the parabola with focus (3,1) and directrix x=7.<BR>\n" );
document.write( "Plot the focus and draw the directrix.<BR>\n" );
document.write( "The vertex is half-way between the focus and the directrix,<BR>\n" );
document.write( "so it is (5,1)<BR>\n" );
document.write( "So h = 5, k = 1, p = -2<BR>\n" );
document.write( "Form for a parabola opening to the left:<BR>\n" );
document.write( "(y-k)^2 = 4p(x-h)<BR>\n" );
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document.write( "Your Problem:<BR>\n" );
document.write( "(y-1)^2 = -8(x-5)<BR>\n" );
document.write( "y^2-2y+1 = -8x+40<BR>\n" );
document.write( "y^2-2y-39 = -8x<BR>\n" );
document.write( "x = (-1/8)(y^2-2y-39)<BR>\n" );
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document.write( "Part B) H is the hyperbola with center at (1,1), an x-intercept at (2,0) and one vertex at (5/4,1). <BR>\n" );
document.write( "Plot the two points:<BR>\n" );
document.write( "h=1 , k=1<BR>\n" );
document.write( "a = 5/4-1 = 1/4<BR>\n" );
document.write( "Form:<BR>\n" );
document.write( "(x-h)^2/a^2 - (y-k)^2/b^2 = 1<BR>\n" );
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document.write( "Your Problem:<BR>\n" );
document.write( "(x-1)^2/(1/4)^2 - (y-1)^2/b^2 = 1<BR>\n" );
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document.write( "Let (x,y) = (2,0)<BR>\n" );
document.write( "(2-1)^2/(1/16) - (0-1)^2/b^2 = 1<BR>\n" );
document.write( "16 - 1/b^2 = 1<BR>\n" );
document.write( "1/b^2 = 15<BR>\n" );
document.write( "b^2 = 1/15<BR>\n" );
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document.write( "Equation:<BR>\n" );
document.write( "16(x-1)^2 - 15(y-1)^2 = 1<BR>\n" );
document.write( "=============================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H. \r<BR>\n" );
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document.write( " </SPAN>\n" );
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