What is the eccentricity 9x^2-4y^2-90x-32y=-305 ?

The eccentricity 9x^2-4y^2-90x-32y=-305 is (sqrt(13))/3

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eccentricity 9x^2-4y^2-90x-32y=-305

eccentricity

9 x^{2} - 4 y^{2} - 90 x - 32 y = - 305

\frac{13}{3}

Solution steps

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

Calculate Hyperbola properties

9 x^{2} - 4 y^{2} - 90 x - 32 y = - 305 :

Up-down Hyperbola with

(h, k) = (5, - 4), a = 6, b = 4

= \frac{6 ^{2} + 4 ^{2}}{6}

Refine

= \frac{13}{3}

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

\frac{x ^{2}}{27} - \frac{y ^{2}}{72} = 1

\frac{x ^{2}}{36} - \frac{y ^{2}}{9} = 1

25 x^{2} - 36 y^{2} = 900

\frac{x ^{2}}{16} - \frac{y ^{2}}{81} = 1

What is the eccentricity 9x^2-4y^2-90x-32y=-305 ?
The eccentricity 9x^2-4y^2-90x-32y=-305 is (sqrt(13))/3