What is the eccentricity (x^2)/(49)-(y^2)/(16)=1 ?

The eccentricity (x^2)/(49)-(y^2)/(16)=1 is (sqrt(65))/7

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eccentricity (x^2)/(49)-(y^2)/(16)=1

eccentricity

\frac{x ^{2}}{49} - \frac{y ^{2}}{16} = 1

\frac{65}{7}

Solution steps

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

Calculate Hyperbola properties

\frac{x ^{2}}{49} - \frac{y ^{2}}{16} = 1 :

Right-left Hyperbola with

(h, k) = (0, 0), a = 7, b = 4

= \frac{7 ^{2} + 4 ^{2}}{7}

Refine

= \frac{65}{7}

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

16 x^{2} - 9 y^{2} + 96 x - 72 y + 144 = 0

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

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

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

What is the eccentricity (x^2)/(49)-(y^2)/(16)=1 ?
The eccentricity (x^2)/(49)-(y^2)/(16)=1 is (sqrt(65))/7