document.write( "Question 615752: Write the equation of the hyperbola with vertices (-10,1) and (4,1) \n" ); document.write( "

Algebra.Com's Answer #387315 by jsmallt9(3759) $\"\"$ $\"About$

You can put this solution on YOUR website!
To find the equation for a hyperbola. $\"%28x-h%29%5E2%2Fa%5E2+-+%28y-k%29%5E2%2Fb%5E2+=+1\"$ or $\"%28y-k%29%5E2%2Fa%5E2+-+%28x-h%29%5E2%2Fb%5E2+=+1\"$ , you need to be able to find the center, (h,k), the \"a\" and the \"b\" and you must be able to figure out if the hyperbola is vertically-oriented or horizontally-oriented.

\n" ); document.write( "As you posted it, the problem does not contain enough information. The best you can do is

Determine that the hyperbola is horizontally-oriented since the vertices are \"side-by-side\" instead of above and below each other.
Determine the center because the center is always halfway between the vertices.
Determine the \"a\" since \"a\" is the distance from the center to a vertex.

There is no way to find the \"b\". Usually, in problems like this, you are given either the foci or the asymptotes.

\n" ); document.write( "With the foci you can find the \"c\" and with the \"c\" and the \"a\" you can find \"b\".

\n" ); document.write( "With the asymptotes you can find their slopes. And from the \"a\" and the slopes of the asymptotes you can find \"b\". \n" ); document.write( "

\n" );