document.write( "Question 721973: Find the center, vertices, and foci of the hyperbola and put the equation in standard form (x^2)-(9y^2)+2x-54y-107=0 \n" ); document.write( "

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Find the center, vertices, and foci of the hyperbola and put the equation in standard form
\n" ); document.write( "(x^2)-(9y^2)+2x-54y-107=0
\n" ); document.write( "***
\n" ); document.write( "complete the square:
\n" ); document.write( "(x^2)-(9y^2)+2x-54y-107=0
\n" ); document.write( "(x^2)+2x-(9y^2)-54y-107=0
\n" ); document.write( "(x^2+2x+1)-9(y^2+6y+9)=107+1+-81
\n" ); document.write( "(x+1)^2-9(y+3)^2=27
\n" ); document.write( " $\"%28x%2B1%29%5E2%2F27-%28y%2B3%29%5E2%2F3=1\"$
\n" ); document.write( "This is an equation of a hyperbola with horizontal transverse axis.
\n" ); document.write( "Its standard form: $\"%28x-h%29%5E2%2Fa%5E2-%28y-k%29%5E2%2Fb%5E2=1\"$ , (h,k)=(x,y) coordinates of the center
\n" ); document.write( "For given hyperbola:
\n" ); document.write( "center: (-1,-3)
\n" ); document.write( "a^2=27
\n" ); document.write( "a=√27≈5.2
\n" ); document.write( "vertices: (-1ąa,-3)=(-1ą5.2,-3)=(-6.2,-3) and (4.2,-3)
\n" ); document.write( "..
\n" ); document.write( "c^2=a^2+b^2=27+3=30
\n" ); document.write( "c=√30≈5.5
\n" ); document.write( "foci:(-1ąc,-3)=(-1ą5.5,-3)=(-6.5,-3) and (4.5,-3) \n" ); document.write( "

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