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#### Explanation

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#### Explanation:

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Oct 20, 2017

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#### Explanation:

The equation of the hyperbola is

${x}^{2} / {a}^{2} - {y}^{2} / {b}^{2} = 1$

Comparing this equation to your equation

$25 {x}^{2} - 16 {y}^{2} - 1 = 0$

$25 {x}^{2} - 16 {y}^{2} = 1$

${x}^{2} / {\left(\frac{1}{5}\right)}^{2} - {y}^{2} / {\left(\frac{1}{4}\right)}^{2} = 1$

Therefore,

$a = \frac{1}{5}$

$b = \frac{1}{4}$

$c = \pm \sqrt{{a}^{2} + {b}^{2}} = \pm \sqrt{\frac{1}{25} + \frac{1}{16}} = \pm \frac{\sqrt{41}}{20}$

The center of the hyperbola is $C = \left(0 , 0\right)$

The vertices are $A = \left(\frac{1}{5} , 0\right)$ and $A ' = \left(- \frac{1}{5} , 0\right)$

The foci are $F = \left(\frac{\sqrt{41}}{20} , 0\right)$ and $F ' = \left(- \frac{\sqrt{41}}{20} , 0\right)$

graph{25x^2-16y^2-1=0 [-1.706, 1.712, -0.853, 0.855]}

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