document.write( "Question 849052: I am taking an online class and it did not come with a book! If someone could at least show me how to work it out, that would be much appreciated!\r
\n" ); document.write( "\n" ); document.write( "Find the center, vertices, and foci of the hyperbola given by the equation (y-6)^2/4 - (x-4)^2/5 = 1. \n" ); document.write( "
Algebra.Com's Answer #511367 by ewatrrr(24785)\"\" \"About 
You can put this solution on YOUR website!
 
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document.write( "Hi,
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document.write( "\"%28y-k%29%5E2%2Fb%5E2+-+%28x-h%29%5E2%2Fa%5E2+=+1\"
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document.write( " \"%28y-6%29%5E2%2F2%5E2+-+%28x-4%29%5E2%2F5+=+1+\"
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document.write( "C(4,6)  Note: x = 4, 
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document.write( "V(4,8) and V(4,4)
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document.write( "Foci: \"sqrt%28a%5E2%2Bb%5E2%29\" = \"sqrt%2810%29\" Foci are: (4, 6+sqrt(10), (4, 6-sqrt(10))\r
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document.write( "Standard Form of an Equation of an Hyperbola opening up and down is:
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document.write( "  \"%28y-k%29%5E2%2Fb%5E2+-+%28x-h%29%5E2%2Fa%5E2+=+1\" with C(h,k) and vertices 'b' units up and down from center,  2b the length of the transverse axis
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document.write( "Foci \"sqrt%28a%5E2%2Bb%5E2%29\"units units up and down from center, along x = h
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document.write( "& Asymptotes Lines passing thru C(h,k), with slopes m =  ± b/a\r
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document.write( "Standard Form of an Equation of an Hyperbola opening right and  left is:
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document.write( "  \"%28x-h%29%5E2%2Fa%5E2+-+%28y-k%29%5E2%2Fb%5E2+=+1\" with C(h,k) and vertices 'a' units right and left of center,   2a the length of the transverse axis
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document.write( "Foci are \"sqrt%28a%5E2%2Bb%5E2%29\" units right and left of center along y = k
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document.write( "& Asymptotes Lines passing thru C(h,k), with slopes  m =  ± b/a 
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