What is the eccentricity (y^2)/(25)-((x+1)^2)/(16)=1 ?

The eccentricity (y^2)/(25)-((x+1)^2)/(16)=1 is (sqrt(41))/5

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eccentricity (y^2)/(25)-((x+1)^2)/(16)=1

eccentricity

\frac{y ^{2}}{25} - \frac{( x + 1 ) ^{2}}{16} = 1

\frac{41}{5}

Solution steps

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

Calculate Hyperbola properties

\frac{y ^{2}}{25} - \frac{( x + 1 ) ^{2}}{16} = 1 :

Up-down Hyperbola with

(h, k) = (- 1, 0), a = 5, b = 4

= \frac{5 ^{2} + 4 ^{2}}{5}

Refine

= \frac{41}{5}

+ \frac{y ^{2}}{16} - \frac{x ^{2}}{9} = 1

\frac{y ^{2}}{36} - \frac{x ^{2}}{9} = 1

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

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

\frac{y ^{2}}{4} - \frac{x ^{2}}{5} = 1

What is the eccentricity (y^2)/(25)-((x+1)^2)/(16)=1 ?
The eccentricity (y^2)/(25)-((x+1)^2)/(16)=1 is (sqrt(41))/5