What is the eccentricity 36x^2-49y^2=1 ?

The eccentricity 36x^2-49y^2=1 is (sqrt(85))/7

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eccentricity 36x^2-49y^2=1

eccentricity

36 x^{2} - 49 y^{2} = 1

\frac{85}{7}

Solution steps

= \frac{a ^{2} + b ^{2}}{a}

Calculate Hyperbola properties

36 x^{2} - 49 y^{2} = 1 :

Right-left Hyperbola with

(h, k) = (0, 0), a = \frac{1}{6}, b = \frac{1}{7}

= \frac{( \frac{1}{6} ) ^{2} + ( \frac{1}{7} ) ^{2}}{\frac{1}{6}}

Refine

= \frac{85}{7}

\frac{y ^{2}}{4} - \frac{x ^{2}}{9} = 1

\frac{y ^{2}}{9} - \frac{x ^{2}}{4} = 1

x^{2} - 4 y^{2} = 16

2 x^{2} - 4 y^{2} = 1

9 x^{2} - 4 y^{2} - 18 x - 16 y - 43 = 0

What is the eccentricity 36x^2-49y^2=1 ?
The eccentricity 36x^2-49y^2=1 is (sqrt(85))/7