document.write( "Question 746309: find an equations for the conic section that satisfies the given conditions. Hyperbola, foci (2,0), (2,8) asymptose y=3+1/2x y=5-1/2x
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Algebra.Com's Answer #455024 by lwsshak3(11628)\"\" \"About 
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find an equations for the conic section that satisfies the given conditions. Hyperbola, foci (2,0), (2,8) asymptose y=3+1/2x y=5-1/2x
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\n" ); document.write( "\n" ); document.write( "Given hyperbola has a vertical transverse axis (y-coordinates of foci change but x-coordinates do not)
\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-
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\n" ); document.write( "center: (2,4)
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\n" ); document.write( "c=4 (distance from center to foci
\n" ); document.write( "c^2=16
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\n" ); document.write( "given slopes of asymptotes=±1/2=a/b (for hyperbolas with vertical transverse axis)
\n" ); document.write( "a/b=1/2
\n" ); document.write( "b=2a
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\n" ); document.write( "c^2=a^2+b^2
\n" ); document.write( "c^2=a^2+4a^2=5a^2
\n" ); document.write( "5a^2=16
\n" ); document.write( "a^2=16/5
\n" ); document.write( "a=4/√5
\n" ); document.write( "b^2=64√5
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\n" ); document.write( "Equation of given hyperbola:
\n" ); document.write( "\"5%28y-4%29%5E2%2F16-5%28x-2%29%5E2%2F64=1\"\r
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