What is the equation of a hyperbola with a=6 and c=9?

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What is the equation of a hyperbola with a=6 and c=9?

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Answer 1 · 2015-06-05T19:02:44

$c^{2} = a^{2} + b^{2}$ $c^2=a^2+b^2$ $\Rightarrow$ $=>$ $9^{2} = 6^{2} + b^{2}$ $9^2=6^2+b^2$ $\Rightarrow$ $=>$ $b^{2} = 81 - 36$ $b^2 = 81-36$ $\Rightarrow$ $=>$ $b^{2} = 45$ $b^2=45$ $\Rightarrow$ $=>$ $b = \pm 3 \sqrt{5}$ $b=+-3sqrt(5)$

$\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1$ $x^2/a^2 - y^2/b^2 = 1$ $\Rightarrow$ $=>$ $\frac{x^{2}}{36} - \frac{y^{2}}{45} = 1$ $x^2/36 - y^2/45 =1$ , that is the equation of the hyperbola.

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What is the equation of a hyperbola with a=6 and c=9?

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