Answer
False statement
Work Step by Step
Identify $a\text{ and }b$ in equation $\frac{{{x}^{2}}}{25}-\frac{{{y}^{2}}}{9}=1$.
$\frac{{{x}^{2}}}{{{\left( 5 \right)}^{2}}}-\frac{{{y}^{2}}}{{{\left( 3 \right)}^{2}}}=1$
Since ${{a}^{2}}>{{b}^{2}}$, the equation of the hyperbola will be horizontal.
Since $a=5\text{ and }b=3$, the x-intercepts are $\left( -5,0 \right)\text{ and }\left( 5,0 \right)$ and the y-intercepts are $\left( 0,-3 \right)\text{ and }\left( 0,3 \right)$.
Plot the points and connect them with the oval shape curve.
Thus, the equation $\frac{{{x}^{2}}}{25}-\frac{{{y}^{2}}}{9}=1$, so it is a false statement.
