What is the eccentricity 9x^2-4y^2+54x+16y+29=0 ?

The eccentricity 9x^2-4y^2+54x+16y+29=0 is (sqrt(13))/2

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

eccentricity

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

\frac{13}{2}

Solution steps

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

Calculate Hyperbola properties

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

Right-left Hyperbola with

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

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

Refine

= \frac{13}{2}

36 x^{2} - 49 y^{2} = 1

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

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

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

2 x^{2} - 4 y^{2} = 1

What is the eccentricity 9x^2-4y^2+54x+16y+29=0 ?
The eccentricity 9x^2-4y^2+54x+16y+29=0 is (sqrt(13))/2