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)![]() ![]() ![]() 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( " |