\frac{9x^{2}}{25}+\frac{9y^{2}}{16}=1
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MathBot Answer:
\(\frac{9 {x}^{2}}{25} + \frac{9 {y}^{2}}{16} = 1\) is an equation of an ellipse, and is equivalent to \(\frac{9 x^{2}}{25} + \frac{9 y^{2}}{16} = 1\).
It is centered at \(\left(0, 0\right)\).
Its foci are \(\left(-1, 0\right)\) and \(\left(1, 0\right)\).
Its minor axis has length \(\frac{8}{3}\) with endpoints \(\left(0, - \frac{4}{3}\right)\) and \(\left(0, \frac{4}{3}\right)\).
Its major axis has length \(\frac{10}{3}\) with endpoints \(\left(- \frac{5}{3}, 0\right)\) and \(\left(\frac{5}{3}, 0\right)\).
The ellipse has parameterization: \[\begin{aligned}x\left(\theta\right) &= \frac{5 \cos{\left(\theta \right)}}{3}\\y\left(\theta\right) &= \frac{4 \sin{\left(\theta \right)}}{3}\end{aligned}\]