document.write( "Question 888569: Find an equation of a hyperbola having foci at (5-√13,-1) and (5+√13,-1) and assymptotes at y=2/3x-13/3 and y=-2/3x+7/3 \n" ); document.write( "

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Find an equation of a hyperbola having foci at (5-√13,-1) and (5+√13,-1) and asymptotes at y=2/3x-13/3 and y=-2/3x+7/3
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\n" ); document.write( "hyperbola has a horizontal transverse axis.
\n" ); document.write( "Its standard form of equation: $\"%28x-h%29%5E2%2Fa%5E2-%28y-k%29%5E2%2Fb%5E2=1\"$ , (h,k)=coordinates of center
\n" ); document.write( "slopes of asymptotes=ą2/3=b/a
\n" ); document.write( "b=ą2a/3
\n" ); document.write( "b^2=4a^2/9
\n" ); document.write( "center: (5,-1)
\n" ); document.write( "c=√13
\n" ); document.write( "c^2=13=a^2+b^2
\n" ); document.write( "a^2+4a^2/9=13
\n" ); document.write( "9a^2+4a^2=117
\n" ); document.write( "13a^2=117
\n" ); document.write( "a^2=9
\n" ); document.write( "b^2=4a^2/9=36/9=4
\n" ); document.write( "equation: $\"%28x-5%29%5E2%2F9-%28y%2B1%29%5E2%2F4=1\"$
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