document.write( "Question 848088: Find the vertices,foci,and asymptotes of the hyperbola. Then sketch the graph ((y^2)/(16))-((x^2)/(4))=1 \n" ); document.write( "
Algebra.Com's Answer #511474 by lwsshak3(11628)\"\" \"About 
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Find the vertices,foci,and asymptotes of the hyperbola. Then sketch the graph
\n" ); document.write( "((y^2)/(16))-((x^2)/(4))=1
\n" ); document.write( "***
\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=1\", (h,k)=(x,y) coordinates of center.
\n" ); document.write( "center: ((0,0)
\n" ); document.write( "a^2=16
\n" ); document.write( "a=4
\n" ); document.write( "vertices: (0±a,0)=(0±4,0)=(-4,0) and (4,0)
\n" ); document.write( "b^2=4
\n" ); document.write( "b=2
\n" ); document.write( "c^2=a^2+b^2=16+4=20
\n" ); document.write( "c≈√20≈4.5
\n" ); document.write( "foci: (0±c,0)=(0±4.5,0)=(-4.5,0) and (4.5,0)
\n" ); document.write( "slope of asymptotes=±a/b=±4/2=±2
\n" ); document.write( "Equation of asymptotes:
\n" ); document.write( "y=2x
\n" ); document.write( "y=-2x\r
\n" ); document.write( "\n" ); document.write( "see graph below:
\n" ); document.write( "y=4(1+x^2/4)^.5\r
\n" ); document.write( "\n" ); document.write( "\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
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