What is the eccentricity 9x^2-16y^2=4 ?

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

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eccentricity 9x^2-16y^2=4

eccentricity

9 x^{2} - 16 y^{2} = 4

\frac{5}{4}

Solution steps

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

Calculate Hyperbola properties

9 x^{2} - 16 y^{2} = 4 :

Right-left Hyperbola with

(h, k) = (0, 0), a = \frac{2}{3}, b = \frac{1}{2}

= \frac{( \frac{2}{3} ) ^{2} + ( \frac{1}{2} ) ^{2}}{\frac{2}{3}}

Refine

= \frac{5}{4}

\frac{x ^{2}}{27} - \frac{y ^{2}}{360} = 1

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

\frac{x ^{2}}{49} - \frac{y ^{2}}{4} = 1

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

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