document.write( "Question 825983: Graph hyperbola \"9y%5E2-x%5E2=1\". Find the foci and asymptotes. \n" ); document.write( "
Algebra.Com's Answer #497856 by math-vortex(648)\"\" \"About 
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document.write( "Hi, there--\r\n" );
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document.write( "THE PROBLEM:\r\n" );
document.write( "Graph hyperbola 9y^2-x^2=1. Find the foci and asymptotes.\r\n" );
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document.write( "A SOLUTION:\r\n" );
document.write( "The general equation for a hyperbola is \"%28x-h%29%5E2%2Fa%5E2-%28y-k%29%5E2%2Fb%5E2=1\" when the transverse axis is horizontal.\r\n" );
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document.write( "If the equation is of the form \"%28y-k%29%5E2%2Fa%5E2-%28x-h%29%5E2%2Fb%5E2=1\" then the transverse axis is vertical.\r\n" );
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document.write( "Your equation is \"9y%5E2-x%5E2=1\". We see that it is the second type, so the transverse axis is vertical. The graph looks kind of like two parabolas, one opening up, the other down.\r\n" );
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document.write( "Find the Center:\r\n" );
document.write( "Next we see that h=0 and k=0. This tells us the the hyperbola is centered at the point\r\n" );
document.write( " (h,k) = (0,0).\r\n" );
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document.write( "Find Vertices and Foci:\r\n" );
document.write( "To find the vertices and foci, we need to calculate a, b, and c. We see right away that b^2 = 1 \r\n" );
document.write( "and b=1,  but we need to do a little work to find a. We need to move the coefficient of y^2 \r\n" );
document.write( "without changing its value.\r\n" );
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document.write( "\"9y%5E2=y%5E2%2F%281%2F9%29\" so \"a%5E2=1%2F9\" and \"a=1%2F3\".\r\n" );
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document.write( "Now find c.\r\n" );
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document.write( "\"c%5E2=a%5E2%2Bb%5E2\"\r\n" );
document.write( "\"c%5E2=1%2B1%2F9\"\r\n" );
document.write( "\"c%5E2=10%2F9\"\r\n" );
document.write( "\"c=sqrt%2810%29%2F3\"\r\n" );
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document.write( "The vertices and foci are located to the above and below the center (because the transverse \r\n" );
document.write( "axis is vertical.)\r\n" );
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document.write( "The foci are the points (0,c)=(0,1) and (0.-c)=(0,-1).\r\n" );
document.write( "The vertices are the points (0,a)=( 0, 1/3) and (0,-a)=(0,-1/3).\r\n" );
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document.write( "Find Asymptotes:\r\n" );
document.write( "When the transverse axis is vertical, the formulas for the two asymptotes are\r\n" );
document.write( "\"y=%28a%2Fb%29%28x-h%29%2Bk\" and \"y=-%28a%2Fb%29%28x-h%29%2Bk\" \r\n" );
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document.write( "You asymptotes are\r\n" );
document.write( "\"y=%281%2F3%29x\" and \"y=-%281%2F3%29x\"\r\n" );
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document.write( "Graph the Hyperbola:\r\n" );
document.write( "This is the graph of the hyperbola and the asymptotes.\r\n" );
document.write( "y=(1/3)sqrt(x^2+1)\r\n" );
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document.write( "Hope this helps! Feel free to email if you have any questions about the solution.\r\n" );
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document.write( "Good luck with your math,\r\n" );
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document.write( "Mrs. F\r\n" );
document.write( "math.in.the.vortex@gmail.com\r\n" );
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