document.write( "Question 604752: Graph the equation. Identify the vertices, foci, and asymptotes of the hyperbola. y^2/16-x^2/36=1 \n" ); document.write( "
Algebra.Com's Answer #381410 by lwsshak3(11628)\"\" \"About 
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Graph the equation. Identify the vertices, foci, and asymptotes of the hyperbola.
\n" ); document.write( "y^2/16-x^2/36=1
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\n" ); document.write( "This is an equation of a hyperbola with vertical transverse axis.
\n" ); document.write( "Its standard form: (y-k)^2/a^2-(x-h)^2/b^2=1, (h,k)=(x,y) coordinates of center
\n" ); document.write( "For given hyperbola: y^2/16-x^2/36=1
\n" ); document.write( "center: (0,0)
\n" ); document.write( "a^2=16
\n" ); document.write( "a=√16=4
\n" ); document.write( "vertices:(0,0±a)=(0,0±4)=(0,-4) and (0,4)
\n" ); document.write( "..
\n" ); document.write( "b^2=36
\n" ); document.write( "b=√36=6
\n" ); document.write( "..
\n" ); document.write( "c^2=a^2+b^2=16+36=52
\n" ); document.write( "c=√52≈7.2
\n" ); document.write( "foci: (0,0±c)=(0,0±7.2)=(0,-7.2) and (0,7.2)
\n" ); document.write( "..
\n" ); document.write( "Asymptotes:
\n" ); document.write( "slope=±a/b=±4/6=±2/3
\n" ); document.write( "equation of asymptotes:
\n" ); document.write( "y=±2x/3
\n" ); document.write( "..
\n" ); document.write( "y=±(16+4x^2/9)^.5
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