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{41}{5}

Decimal

1.28062 \dots

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}

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