document.write( "Question 1047763: sketch the hyperbola and label the vertices,foci and asymptotes of x²-4y²+2x+8y-7=0 \n" ); document.write( "

Algebra.Com's Answer #663431 by ewatrrr(24785) $\"\"$ $\"About$

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x²-4y²+2x+8y-7=0
\n" ); document.write( "complete Squares
\n" ); document.write( "(x+1)^2 - 4(y-1)^2 = 7+ 1 - 4
\n" ); document.write( " $\"%28x%2B1%29%5E2+%2F4-+%28y-1%29%5E2%2F1+=1\"$
\n" ); document.write( "Opens left and right along y = 1
\n" ); document.write( "C(-1,1) , a = 2
\n" ); document.write( "V(1,1) and (-3,1)
\n" ); document.write( "|
\n" ); document.write( "foci
\n" ); document.write( "sqrt(4 + 1) = sqrt5\r
\n" ); document.write( "\n" ); document.write( "F(-1 + √5, 1) and F(-1-√5, 1)
\n" ); document.write( "|
\n" ); document.write( "Asymptotes
\n" ); document.write( "m = ± 1/2
\n" ); document.write( "y - 1 = (1/2)(x+1)
\n" ); document.write( "y = (1/2)x + 3/2
\n" ); document.write( "0r
\n" ); document.write( "y - 1 = -(1/2)(x+1)
\n" ); document.write( "y= -(1/2)x + 1/2
\n" ); document.write( "____________________________________________________________________________
\n" ); document.write( "Need to Know
\n" ); document.write( "Standard Form of an Equation of an Hyperbola opening right and left is:
\n" ); 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. e = c/a.
\n" ); document.write( "Foci are $\"sqrt%28a%5E2%2Bb%5E2%29\"$ = c- units right and left of center along y = k
\n" ); document.write( "& Asymptotes Lines passing thru C(h,k), with slopes m = ± b/a
\n" ); document.write( "ow:
\n" ); document.write( " \n" ); document.write( "

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