document.write( "Question 854643: Find the vertices, foci, and center of the hyperbola. Graph the equation.
\n" ); document.write( "4y^2 - x^2 - 2x - 16y + 11 = 0 \n" ); document.write( "
Algebra.Com's Answer #514808 by lwsshak3(11628)\"\" \"About 
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Find the vertices, foci, and center of the hyperbola. Graph the equation.
\n" ); document.write( "4y^2 - x^2 - 2x - 16y + 11 = 0
\n" ); document.write( "4y^2-16y -x^2-2x=-11
\n" ); document.write( "complete the square:
\n" ); document.write( "4(y^2-4y+4) -(x^2+2x+1)=-11+16-1
\n" ); document.write( "4(y-2)^2-(x+1)^2=4
\n" ); document.write( "\"%28y-2%29%5E2-%28x%2B1%29%5E2%2F4=1\"
\n" ); document.write( "This is an equation of a hyperbola with vertical transverse axis.
\n" ); document.write( "Its standard form of equation: \"%28y-k%29%5E2%2Fa%5E2-%28x-h%29%5E2%2Fb%5E2\", (h,k)=coordinates of center
\n" ); document.write( "For given hyperbola:
\n" ); document.write( "center: (-1,2)
\n" ); document.write( "a^2=1
\n" ); document.write( "a=1
\n" ); document.write( "vertices: (-1,2±a)=(-1,2±1)=(-1,1) and (-1,3)
\n" ); document.write( "b^2=4
\n" ); document.write( "b=2
\n" ); document.write( "c^2=a^2+b^2=1+4=5
\n" ); document.write( "c=√5≈2.2
\n" ); document.write( "foci: (-1,2±c)=(-1,2±2.2)=(-1,-.2) and (-1,4.2)
\n" ); document.write( "see graph below:
\n" ); document.write( "y=(1+(x+1)^2/4)^.5+2
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