document.write( "Question 610053: What are the vertices of the hyperbola given by the equation (y^2/81)-(x^2/49)=1? \n" ); document.write( "
Algebra.Com's Answer #384155 by KMST(5328)\"\" \"About 
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With the equation y^2/81-x^2/49=1 or \"y%5E2%2F81-x%5E2%2F49=1\"
\n" ); document.write( "(I believe in parentheses, but you did not need those),
\n" ); document.write( "you realize that your hyperbola is symmetrical to either side of the y-axis
\n" ); document.write( "(because what's valid for any value of x is valid for -x)
\n" ); document.write( "and it is symmetrical to either side of the x-axis
\n" ); document.write( "(because what's valid for any value of y is valid for -y).
\n" ); document.write( "As a consequence, it must be centered at the origin.
\n" ); document.write( "You also realize that y=0 is impossible, because it would mean that a negative number equals 1:
\n" ); document.write( "-x^2/49=1
\n" ); document.write( "So your hyperbola does not touch the x-axis (where y=0).
\n" ); document.write( "Then it must graph as a smile-shaped curve above the x-axis, and the symmetrical \"frown\" below the x-axis, with vertices at (0,b) and (0,-b).
\n" ); document.write( "If you make x=0, you get y^2/81=1, and from there you find
\n" ); document.write( "y^2=81, and the coordinates of the vertices as y=9 and y=-9.
\n" ); document.write( "So the vertices are (0,9) and (0,-9). \n" ); document.write( "
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