What is the eccentricity (y^2}{16}-\frac{x^2)/9 =1 ?

The eccentricity (y^2}{16}-\frac{x^2)/9 =1 is 5/4

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eccentricity (y^2}{16}-\frac{x^2)/9 =1

eccentricity

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

\frac{5}{4}

Solution steps

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

Calculate Hyperbola properties

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

Up-down Hyperbola with

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

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

Refine

= \frac{5}{4}

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

\frac{y ^{2}}{16} - \frac{x ^{2}}{25} = 1

4 x^{2} - 9 y^{2} = 36

\frac{( x - 2 ) ^{2}}{9} - \frac{( y + 1 ) ^{2}}{5} = 1

\frac{x ^{2}}{144} - \frac{y ^{2}}{25} = 1

What is the eccentricity (y^2}{16}-\frac{x^2)/9 =1 ?
The eccentricity (y^2}{16}-\frac{x^2)/9 =1 is 5/4