Determine if the transverse axis is horizontal or vertical for the following hyperbolas.
A
Horizontal
B
Vertical
C
Cannot be determined
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1
Recall the standard form of a hyperbola equation: for a horizontal transverse axis, it is \(\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1\), and for a vertical transverse axis, it is \(\frac{y^2}{a^2} - \frac{x^2}{b^2} = 1\).
Compare the given equation \(\frac{y^2}{9} - \frac{x^2}{9} = 1\) to the standard forms to identify which variable's term is positive and which is negative.
Notice that the \(y^2\) term is positive and the \(x^2\) term is negative, matching the form \(\frac{y^2}{a^2} - \frac{x^2}{b^2} = 1\).
Since the positive term corresponds to \(y^2\), the transverse axis is vertical (along the y-axis).
Conclude that the hyperbola has a vertical transverse axis based on the position of the positive term in the equation.