document.write( "Question 698158: what is a possible equation for a hyperbola that is centered at the origin, opens left and right and has a transverse axis of length 6 \n" ); document.write( "

Algebra.Com's Answer #430586 by KMST(5328) $\"\"$ $\"About$

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A hyperbola that is centered at the origin, and opens left and right has an equation of the form
\n" ); document.write( " $\"x%5E2%2Fa%5E2-y%5E2%2Fb%5E2=1\"$
\n" ); document.write( "where $\"x\"$ cannot be zero (because it would mean $\"-y%5E2%2Fb%5E2=1\"$ <---> $\"y%5E2%2Fb%5E2=-1\"$ ,
\n" ); document.write( "but when $\"y=0\"$ , $\"x%5E2%2Fa%5E2=1\"$ <---> $\"x%5E2=a%5E2\"$ , so $\"x=a\"$ or $\"x=-a\"$ Those are the x-coordinates of vertices (-a,0) and (a,0),
\n" ); document.write( "and the distance between the vertices is the transverse axis = $\"2a\"$
\n" ); document.write( "So the equation you need is
\n" ); document.write( " $\"highlight%28x%5E2%2F3%5E2-y%5E2%2Fb%5E2=1%29\"$ or $\"highlight%28x%5E2%2F9-y%5E2%2Fb%5E2=1%29\"$
\n" ); document.write( "You can chose a value for $\"b%5E2\"$ to change how \"pointy\" the vertices are.
\n" ); document.write( "The slopes of the asymptotes will be $\"b%2Fa\"$ and $\"-b%2Fa\"$
\n" ); document.write( " \n" ); document.write( "

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