document.write( "Question 600340: find the foci, vertices, equations of the asyptotes, length of the transverse axis, and the length of the conjugate axis for the hyperbola 16y^2-x^2=16. \n" ); document.write( "
Algebra.Com's Answer #379407 by lwsshak3(11628)\"\" \"About 
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find the foci, vertices, equations of the asymptotes, length of the transverse axis, and the length of the conjugate axis for the hyperbola
\n" ); document.write( "16y^2-x^2=16
\n" ); document.write( "divide by 16
\n" ); document.write( "y^2-x^2/16=1
\n" ); document.write( "This is an equation of a hyperbola with vertical transverse axis (y-term listed ahead of x-term)
\n" ); document.write( "Its standard form: (y-h)^2/a^2-(y-k)^2/b^2=1, (h,k)=(x,y) coordinates of center
\n" ); document.write( "For given equation:
\n" ); document.write( "center: (0,0)
\n" ); document.write( "..
\n" ); document.write( "a^2=1
\n" ); document.write( "a=1
\n" ); document.write( "length of vertical transverse axis=2a=2
\n" ); document.write( "Vertices: (0,0±a)=(0,0±1)=(0,1) and (0,-1)
\n" ); document.write( "..
\n" ); document.write( "b^2=16
\n" ); document.write( "b=√16=4
\n" ); document.write( "length of conjugate axis=2b=8
\n" ); document.write( "..
\n" ); document.write( "Foci:
\n" ); document.write( "c^2=a^2+b^2=1+16=17
\n" ); document.write( "c=√17≈4.1
\n" ); document.write( "Foci: (0,0±c)=(0,0±4.1)=(0,4.1) and (0,-4.1)
\n" ); document.write( "..
\n" ); document.write( "Asymptotes:
\n" ); document.write( "Asymptotes are straight lines that go thru the center(0,0)
\n" ); document.write( "Equation: y=mx+b, m=slope, b=y-intercept
\n" ); document.write( "slopes:±a/b=±1/4
\n" ); document.write( "y=x/4+b
\n" ); document.write( "since asymptotes go thru the origin, b=0
\n" ); document.write( "Equations of asymptotes:
\n" ); document.write( "y=x/4
\n" ); document.write( "y=-x/4 \n" ); document.write( "
\n" );