What is the eccentricity 4y^2-9x^2+8y-54x-113=0 ?

The eccentricity 4y^2-9x^2+8y-54x-113=0 is (sqrt(13))/3

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eccentricity 4y^2-9x^2+8y-54x-113=0

eccentricity

4 y^{2} - 9 x^{2} + 8 y - 54 x - 113 = 0

\frac{13}{3}

Solution steps

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

Calculate Hyperbola properties

4 y^{2} - 9 x^{2} + 8 y - 54 x - 113 = 0 :

Up-down Hyperbola with

(h, k) = (- 3, - 1), a = 3, b = 2

= \frac{3 ^{2} + 2 ^{2}}{3}

Refine

= \frac{13}{3}

\frac{x ^{2}}{36} - \frac{y ^{2}}{4} = 1

\frac{x ^{2}}{40} - \frac{y ^{2}}{120} = 1

0 = - \frac{400}{9} x^{2} + 16 y^{2} + 400

\frac{x ^{2}}{121} - \frac{y ^{2}}{81} = 1

\frac{x ^{2}}{27} - \frac{y ^{2}}{216} = 1

What is the eccentricity 4y^2-9x^2+8y-54x-113=0 ?
The eccentricity 4y^2-9x^2+8y-54x-113=0 is (sqrt(13))/3