document.write( "Question 454107: Hi, I am studying for a quiz on hyperbolas and one of the problems I am doing is this:
\n" ); document.write( "Write an equation in standard form for each hyperbola.
\n" ); document.write( "Length of transverse axis 10 and foci at (-7,18) and (-7,-8)\r
\n" ); document.write( "\n" ); document.write( "So far, I understand that it is vertical therefore the equation would be in the (y-k)^2/a^2-(x-h)^2/b^2=1
\n" ); document.write( "I am pretty sure I also got the center which was (-7, 5)
\n" ); document.write( "So now I have (y-5)^2/a^2-(x+7)^2/b^2=1
\n" ); document.write( "My problem is is that I don't know how to find what a and b are. I understand they come from the vertices and co-vertices but I don't think I fully understand the transverse axis.
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Algebra.Com's Answer #311886 by stanbon(75887)\"\" \"About 
You can put this solution on YOUR website!
Write an equation in standard form for each hyperbola.
\n" ); document.write( "Length of transverse axis 10 and foci at (-7,18) and (-7,-8)
\n" ); document.write( "So far, I understand that it is vertical therefore the equation would be in the (y-k)^2/a^2-(x-h)^2/b^2=1
\n" ); document.write( "I am pretty sure I also got the center which was (-7, 5)
\n" ); document.write( "So now I have (y-5)^2/a^2-(x+7)^2/b^2=1
\n" ); document.write( "My problem is is that I don't know how to find what a and b are. I understand they come from the vertices and co-vertices but I don't think I fully understand the transverse axis.
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\n" ); document.write( "Plot the foci points.
\n" ); document.write( "The distance between the foci is 18--8 = 26
\n" ); document.write( "---
\n" ); document.write( "2a + 2c = 26
\n" ); document.write( "But length of transverse axis = 2a = 10
\n" ); document.write( "So, a = 5
\n" ); document.write( "---
\n" ); document.write( "And 2c = 26-10 = 16
\n" ); document.write( "So c = 8
\n" ); document.write( "---
\n" ); document.write( "For a hyperbola a^2+b^2 = c^2
\n" ); document.write( "25 + b^2 = 16
\n" ); document.write( "b^2 = 9
\n" ); document.write( "b = 3
\n" ); document.write( "----
\n" ); document.write( "Since (h,k) = (-7,5)
\n" ); document.write( "Equation:
\n" ); document.write( "(y-5)^2/25 - (x+7)^2/9 = 1
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\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H.
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