What is the eccentricity (x^2)/(16)-(y^2)/(81)=1 ?

The eccentricity (x^2)/(16)-(y^2)/(81)=1 is (sqrt(97))/4

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eccentricity (x^2)/(16)-(y^2)/(81)=1

eccentricity

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

\frac{97}{4}

Solution steps

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

Calculate Hyperbola properties

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

Right-left Hyperbola with

(h, k) = (0, 0), a = 4, b = 9

= \frac{4 ^{2} + 9 ^{2}}{4}

Refine

= \frac{97}{4}

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

x^{2} - y^{2} - 4 x - 6 y - 14 = 0

\frac{x ^{2}}{144} - \frac{y ^{2}}{81} = 1

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

9 x^{2} - 4 y^{2} + 54 x + 16 y + 29 = 0

What is the eccentricity (x^2)/(16)-(y^2)/(81)=1 ?
The eccentricity (x^2)/(16)-(y^2)/(81)=1 is (sqrt(97))/4