Which is a true statement comparing the graphs of \( \frac{x^{2}}{3^{2}}-\frac{y^{2}}{4^{2}}=1 \) and \( \frac{y^{2}}{3^{2}}-\frac{x^{2}}{4^{2}}=1 \) ? The foci of both graphs are the same points. The lengths of both transverse axes are the same. The directices of \( \frac{x^{2}}{3^{2}}-\frac{y^{2}}{4^{2}}=1 \) are horvontal while the directrices of \( \frac{v^{2}}{y^{2}}-\frac{x^{2}}{4^{2}}=1 \) are vertical. The vertices of \( \frac{x^{2}}{3^{2}}-\frac{y^{2}}{4^{2}}=1 \) are on the \( y \)-axis whice the vertices of \( \frac{v^{2}}{3^{2}}-\frac{y^{2}}{4^{2}}=1 \) are on the \( x \)-axis.
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- The equations \( \frac{x^{2}}{3^{2}}-\frac{y^{2}}{4^{2}}=1 \) and \( \frac{y^{2}}{3^{2}}-\frac{x^{2}}{4^{2}}=1 \) are both hyperbolas. Show moreā¦
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The graph of the equation $\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1$ with $a>0, b>0$ is a hyperbola with vertices $(-,-)$ and $(-,-)$ and foci $( \pm c, 0),$ where $c=$ ______ So the graph of $\frac{x^{2}}{4^{2}}-\frac{y^{2}}{3^{2}}=1$ is a hyperbola with vertices $(-,-)$ and $(-,-)$and foci $(-,-)$ and $(-,-)$
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The graph of the equation $\frac{y^{2}}{a^{2}}-\frac{x^{2}}{b^{2}}=1$ with $a>0, b>0$ is a hyperbola with vertices $(-,-)$ and $(-,-)$ and foci $(0, \pm c),$ where $c=$ ______ So the graph of $\frac{y^{2}}{4^{2}}-\frac{x^{2}}{3^{2}}=1$ is a hyperbola with vertices and $(-,-)$ and foci $(-,-)$ and $(-,-)$
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