document.write( "Question 577691: How can someone write an equation for a hyperbola using characteristics such as the foci: (-1,9) (-1,-7) and the conjugate axis has a length of 14 units? \n" ); document.write( "
Algebra.Com's Answer #370662 by lwsshak3(11628)\"\" \"About 
You can put this solution on YOUR website!
How can someone write an equation for a hyperbola using characteristics such as the foci: (-1,9) (-1,-7) and the conjugate axis has a length of 14 units?
\n" ); document.write( "**
\n" ); document.write( "Standard form of an equation for a hyperbola with vertical transverse axis:
\n" ); document.write( "(y-k)^2/a^2-(x-h)^2/b^2=1, (h,k) being the (x,y) coordinates of the center.
\n" ); document.write( "For given hyperbola:
\n" ); document.write( "center:(-1,1)
\n" ); document.write( "given length of conjugate axis=14=2b
\n" ); document.write( "b=7
\n" ); document.write( "b^2=49
\n" ); document.write( "..
\n" ); document.write( "from given foci data, c=(9+(-7))/2=16/2=8 (by midpoint formula)
\n" ); document.write( "c^2=64
\n" ); document.write( "..
\n" ); document.write( "c^2=a^2+b^2
\n" ); document.write( "a^2=c^2-b^2=64-49=15
\n" ); document.write( "a=√15≈3.87
\n" ); document.write( "..
\n" ); document.write( "equation:
\n" ); document.write( "(y-1)^2/15-(x+1)^2/49=1
\n" ); document.write( "
\n" ); document.write( "
\n" );