What is the eccentricity 25x^2+10922x-25y^2-y^2=1439 ?

The eccentricity 25x^2+10922x-25y^2-y^2=1439 is (sqrt(761391648))/(8sqrt(6065007))

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eccentricity 25x^2+10922x-25y^2-y^2=1439

eccentricity

25 x^{2} + 10922 x - 25 y^{2} - y^{2} = 1439

\frac{761391648}{8 6065007}

Solution steps

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

Calculate Hyperbola properties

25 x^{2} + 10922 x - 25 y^{2} - y^{2} = 1439 :

Right-left Hyperbola with

(h, k) = (- \frac{5461}{25}, 0), a = \frac{8 466539}{25}, b = \frac{4 933078}{5 13}

= \frac{( \frac{8 466539}{25} ) ^{2} + ( \frac{4 933078}{5 13} ) ^{2}}{\frac{8 466539}{25}}

Refine

= \frac{761391648}{8 6065007}

16 x^{2} - 9 y^{2} + 32 x + 72 y - 704 = 0

16 y^{2} - 32 y - 9 x^{2} - 18 x = 137

\frac{x ^{2}}{a ^{2}} - \frac{y ^{2}}{b ^{2}} = 1

\frac{y ^{2}}{4} - (x + 1)^{2} = 1

3 x^{2} - 4 y^{2} = 12

What is the eccentricity 25x^2+10922x-25y^2-y^2=1439 ?
The eccentricity 25x^2+10922x-25y^2-y^2=1439 is (sqrt(761391648))/(8sqrt(6065007))