document.write( "Question 721975: Find the standard form of the equation of the hyperbola with vertices (4,1),(4,9) and foci (4,0),(4,10) \n" ); document.write( "
Algebra.Com's Answer #442614 by lwsshak3(11628)\"\" \"About 
You can put this solution on YOUR website!
Find the standard form of the equation of the hyperbola with vertices (4,1),(4,9) and foci (4,0),(4,10)
\n" ); document.write( "**
\n" ); document.write( "Given data shows hyperbola has a vertical transverse axis (y-coordinates change but x-coordinates do not)
\n" ); document.write( "Its standard form of equation: \"%28y-k%29%5E2%2Fa%5E2-%28x-h%29%5E2%2Fb%5E2=1\", (h,k)=(x,y) coordinates of the center.
\n" ); document.write( "x-coordinate of center=4
\n" ); document.write( "y-coordinate of center=5 (midpoint of vertices and foci)
\n" ); document.write( "center: (4,5)
\n" ); document.write( "length of vertical transverse axis=8 (1 to 9)=2a
\n" ); document.write( "a=4
\n" ); document.write( "a^2=16
\n" ); document.write( "Foci:
\n" ); document.write( "2c=10 (0 to 10)
\n" ); document.write( "c=5
\n" ); document.write( "c^2=25
\n" ); document.write( "c^2=a^2+b^2
\n" ); document.write( "b^2=c^2-a^2=25-16=9
\n" ); document.write( "Equation of given hyperbola:
\n" ); document.write( "\"%28y-5%29%5E2%2F16-%28x-4%29%5E2%2F9=1\"
\n" ); document.write( " \n" ); document.write( "
\n" );