What is the eccentricity 9x^2-4y^2-36=0 ?

The eccentricity 9x^2-4y^2-36=0 is (sqrt(13))/2

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eccentricity 9x^2-4y^2-36=0

eccentricity

9 x^{2} - 4 y^{2} - 36 = 0

\frac{13}{2}

Solution steps

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

Calculate Hyperbola properties

9 x^{2} - 4 y^{2} - 36 = 0 :

Right-left Hyperbola with

(h, k) = (0, 0), a = 2, b = 3

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

Refine

= \frac{13}{2}

\frac{x ^{2}}{49} - \frac{y ^{2}}{16} = 1

4 y^{2} - 25 x^{2} = 100

16 x^{2} - 9 y^{2} + 96 x - 72 y + 144 = 0

\frac{( x + 5 ) ^{2}}{4} - \frac{( y - 2 ) ^{2}}{9} = 1

4 x^{2} - 9 y^{2} + 32 x + 36 y + 64 = 0

What is the eccentricity 9x^2-4y^2-36=0 ?
The eccentricity 9x^2-4y^2-36=0 is (sqrt(13))/2