What is the eccentricity 9y^2-16x^2=144 ?

The eccentricity 9y^2-16x^2=144 is 5/4

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eccentricity 9y^2-16x^2=144

eccentricity

9 y^{2} - 16 x^{2} = 144

\frac{5}{4}

Solution steps

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

Calculate Hyperbola properties

9 y^{2} - 16 x^{2} = 144 :

Up-down Hyperbola with

(h, k) = (0, 0), a = 4, b = 3

= \frac{4 ^{2} + 3 ^{2}}{4}

Refine

= \frac{5}{4}

\frac{x ^{2}}{16} - \frac{y ^{2}}{9} = 1

\frac{y ^{2}}{25} - \frac{x ^{2}}{81} = 1

- x^{2} + 9 y^{2} + 4 x + 54 y + 68 = 0

18 x^{2} - 32 y^{2} - 108 y - 128 x - 254 = 0

25 x^{2} + 246 x - 25 y^{2} - 13 y = 233

What is the eccentricity 9y^2-16x^2=144 ?
The eccentricity 9y^2-16x^2=144 is 5/4