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

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

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eccentricity 9(x-2)^2-4y^2=36

eccentricity

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

\frac{13}{2}

Solution steps

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

Calculate Hyperbola properties

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

Right-left Hyperbola with

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

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

Refine

= \frac{13}{2}

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

\frac{x ^{2}}{58} - \frac{y ^{2}}{174} = 1

\frac{x ^{2}}{4} - \frac{y ^{2}}{9} = 1

25 x^{2} + 10922 x - 25 y^{2} - y^{2} = 1439

16 x^{2} - 9 y^{2} + 32 x + 72 y - 704 = 0

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