document.write( "Question 629767: What are the slopes of the asymptotes of a hyperbola with equation (y - 2) squared/ 1 squared - (x- 4) squared/ 3 squared = 1?
\n" ); document.write( " \n" ); document.write( "

Algebra.Com's Answer #396535 by jsmallt9(3758) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"%28y+-+2%29%5E2%2F1%5E2+-+%28x-+4%29%5E2%2F3%5E2+=+1\"$
\n" ); document.write( "The slopes of the asymptotes of a hyperbola are either + $\"a%2Fb\"$ or + $\"b%2Fa\"$ . If you're like me you have trouble which one to use when. This can be figured out, as you'll see shortly.

\n" ); document.write( "From the equation we can tell that

a = 1 (since $\"a%5E2\"$ is always under the first term)
b = 3 (since $\"b%5E2\"$ is always under the first term)
the hyperbola is vertically oriented (since the the first term has \"y\", not \"x\", in it).

On a vertically oriented hyperbola, the a will be a vertical distance (IOW a \"rise\") and the b will be a horizontal distance (IOW, a \"run\"). Since slope is always rise/run we will need to use + $\"a%2Fb\"$ for this hyperbola.

\n" ); document.write( "So the slopes of this particular hyperbola are + $\"1%2F3\"$ \n" ); document.write( "

\n" );