document.write( "Question 722933: find the standard form of the equation of the hyperbola given the Vertices: (2,0), (6,0); Foci: (0,0), (8,0) \n" ); document.write( "
Algebra.Com's Answer #442953 by lwsshak3(11628)\"\" \"About 
You can put this solution on YOUR website!
find the standard form of the equation of the hyperbola given the Vertices: (2,0), (6,0); Foci: (0,0), (8,0)
\n" ); document.write( "***
\n" ); document.write( "given data shows that hyperbola has a horizontal transverse axis: (x-coordinates change but y-coordinates do not)
\n" ); document.write( "standard form of equation of given hyperbola: \"%28x-h%29%5E2%2Fa%5E2-%28y-k%29%5E2=1\", (h.k)=(x,y) coordinates of the center
\n" ); document.write( "x-coordinate of center=4(midpoint of vertices and foci)
\n" ); document.write( "y-cooordinate of center=0
\n" ); document.write( "center: (4,0)
\n" ); document.write( "length of horizontal transverse axis=4 (2 to 6)=2a
\n" ); document.write( "a=2
\n" ); document.write( "a^2=4
\n" ); document.write( "distance between foci=8=2c
\n" ); document.write( "c=4
\n" ); document.write( "c^2=16
\n" ); document.write( "c^2=a^2+b^2
\n" ); document.write( "b^2=c^2-a^2=16-4=12
\n" ); document.write( "equation of given hyperbola: \"%28x-4%29%5E2%2F4-y%5E2%2F12=1\" \n" ); document.write( "
\n" );