document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1010722>Question 1010722</A>: <I><SPAN STYLE=\"word-break: break-all;\"> worlds of fun is designing a new ride the ride has 2 tracks that are hyperbolic if the ride is placed on a coordinate grid the vertices of the ride are at (-3,2) and (5,2) and the foci are at (-5,2) and (7,2) <BR>\n" );
document.write( "explain how to find the values of A,B, and C for the hyperbolic tracks and state their values  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #628203 by </B><A HREF=/tutors/aboutme.mpl?userid=FormerJosephStalin><B>FormerJosephStalin(2)</B></A><img src=\"/images/stars/iconNewId_16x16.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=FormerJosephStalin><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=628203\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Hi, Thanks for the question.\r<BR>\n" );
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document.write( "So the hyperbola has vertices of (-3,2) and (5,2). Since both of the vertices both have the same y-coordinate, this is going to be a horizontal hyperbola. The a-value of the hyperbola represents the distance from the center to the vertices. In order to calculate the center, it is simply the midpoint between the two vertices. \r<BR>\n" );
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document.write( "Recall the midpoint formula<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x1%2Bx2%29%2F2%2C%28y1%2By2%29%2F2%29 ALIGN=MIDDLE  ALT=\"%28x1%2Bx2%29%2F2%2C%28y1%2By2%29%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > So we would so (-3+5)/2 to get our x-coordinate which is 1 and (2+2)/2 to get the y-coordinate of the midpoint which is 2. So the center is (1,2). Since a is the distance between the center and vertices, in this case since (-3,2) is 4 units from (1,2) and (1,2) is 4 units from (5,2). The a-value is 4. \r<BR>\n" );
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document.write( "The c value is the distance from the center to the foci, so (1,2) is 6 units from (7,2) and (1,2) is also 6 units from (-5,2). So c is 6. \r<BR>\n" );
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document.write( "Remember that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2%2Bb%5E2=c%5E2 ALIGN=MIDDLE  ALT=\"a%5E2%2Bb%5E2=c%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > is used to find the foci hyperbola. Since we now know a and c, we can find b. So we will substitute the values into the equation. 4^2+b^2=6^2 So 16 + b^2 = 36 Solving for b, we get the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2820%29 ALIGN=MIDDLE  ALT=\"sqrt%2820%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or 2*<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%285%29 ALIGN=MIDDLE  ALT=\"sqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "In conclusion, a = 4, b = 2*<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%285%29 ALIGN=MIDDLE  ALT=\"sqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and c = 6 \r<BR>\n" );
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document.write( "Hope this helped :) Have a good day!<BR>\n" );
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