What is the eccentricity ((x+5)^2)/4-((y-2)^2)/9 =1 ?

The eccentricity ((x+5)^2)/4-((y-2)^2)/9 =1 is (sqrt(13))/2

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eccentricity ((x+5)^2)/4-((y-2)^2)/9 =1

eccentricity

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

\frac{13}{2}

Solution steps

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

Calculate Hyperbola properties

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

Right-left Hyperbola with

(h, k) = (- 5, 2), a = 2, b = 3

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

Refine

= \frac{13}{2}

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

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

What is the eccentricity ((x+5)^2)/4-((y-2)^2)/9 =1 ?
The eccentricity ((x+5)^2)/4-((y-2)^2)/9 =1 is (sqrt(13))/2