What is the eccentricity 9x^2-36x-4y^2-24y-36=0 ?

The eccentricity 9x^2-36x-4y^2-24y-36=0 is (sqrt(13))/2

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eccentricity 9x^2-36x-4y^2-24y-36=0

eccentricity

9 x^{2} - 36 x - 4 y^{2} - 24 y - 36 = 0

\frac{13}{2}

Solution steps

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

Calculate Hyperbola properties

9 x^{2} - 36 x - 4 y^{2} - 24 y - 36 = 0 :

Right-left Hyperbola with

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

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

Refine

= \frac{13}{2}

\frac{x ^{2}}{16} - \frac{y ^{2}}{20} = 1

16 x^{2} - 25 y^{2} = 400

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

4 x^{2} - y^{2} - 24 x - 4 y + 28 = 0

9 y^{2} - x^{2} + 2 x + 54 y + 62 = 0

What is the eccentricity 9x^2-36x-4y^2-24y-36=0 ?
The eccentricity 9x^2-36x-4y^2-24y-36=0 is (sqrt(13))/2