document.write( "Question 569463: y^2/36-x^2/4=1. find the coordinates of the vertices and foci and the equations of the asymptotes for the hyperbola and graph \n" ); document.write( "
Algebra.Com's Answer #367346 by lwsshak3(11628)\"\" \"About 
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y^2/36-x^2/4=1. find the coordinates of the vertices and foci and the equations of the asymptotes for the hyperbola and graph.
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\n" ); document.write( "Standard form of equation for a hyperbola with vertical transverse axis:
\n" ); document.write( "(y-k)^2/a^2-(x-h)^2/b^2=1, with (h,k) being the (x,y) coordinates of the center.
\n" ); document.write( "..
\n" ); document.write( "For given hyperbola, y^2/36-x^2/4=1.
\n" ); document.write( "center: (0,0)
\n" ); document.write( "a^2=36
\n" ); document.write( "a=√36=6
\n" ); document.write( "vertices: (0,0±a)=(0,±6)=(0,-6) and (0,6)
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\n" ); document.write( "b^2=4
\n" ); document.write( "b=2
\n" ); document.write( "c^2=a^2+b^2=36+4=40
\n" ); document.write( "c=√40≈6.32
\n" ); document.write( "Foci: (0,0±c)=(0,±√40)=(0,-6.32) and (0,6.32)
\n" ); document.write( "..
\n" ); document.write( "Asymptotes:
\n" ); document.write( "slope of asymptotes: ±a/b=±6/2=±3
\n" ); document.write( "equation of asymptotes: y=3x and y=-3x
\n" ); document.write( "see graph below:
\n" ); document.write( "y=(36+9x^2)^.5
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