document.write( "Question 712796: Equation of a hyberbola\r
\n" ); document.write( "\n" ); document.write( "(x-3)^2 over 4 - (y+2)^2 over 9 = 1\r
\n" ); document.write( "\n" ); document.write( "How do I find the vertices, foci, and asymptote slope? \n" ); document.write( "

Algebra.Com's Answer #438270 by lwsshak3(11628) $\"\"$ $\"About$

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Equation of a hyberbola
\n" ); document.write( "(x-3)^2 over 4 - (y+2)^2 over 9 = 1
\n" ); document.write( "How do I find the vertices, foci, and asymptote slope?
\n" ); document.write( "**
\n" ); document.write( "Standard form of equation for a hyperbola with horizontal transverse axis:
\n" ); document.write( " $\"%28x-h%29%5E2%2Fa%5E2-%28y-k%29%5E2%2Fb%5E2=1\"$ , (h,k)=(x,y) coordinates of center.
\n" ); document.write( "..
\n" ); document.write( "For given problem:
\n" ); document.write( "equation: $\"%28x-3%29%5E2%2F4-%28y%2B2%29%5E2%2F9=1\"$
\n" ); document.write( "center: (3,-2)
\n" ); document.write( "a^2=4
\n" ); document.write( "a=2
\n" ); document.write( "vertices: (3ąa,-2)=(3ą2,-2)=(1,-2) and (5,-2)
\n" ); document.write( "..
\n" ); document.write( "b^2=9
\n" ); document.write( "b=3
\n" ); document.write( "..
\n" ); document.write( "c^2=a^2+b^2=4+9=13
\n" ); document.write( "c=√13≈3.6
\n" ); document.write( "foci: (3ąc,-2)=(3ą3.6,-2)=(-0.6,-2) and (6.6,-2)
\n" ); document.write( "..
\n" ); document.write( "slopes of asymptotes of hyperbolas with horizontal transverse axis: ąb/a=ą3/2\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

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