What is the eccentricity 49x^2-25y^2-686x-50y+2375=0 ?

The eccentricity 49x^2-25y^2-686x-50y+2375=0 is (sqrt(74))/5

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eccentricity 49x^2-25y^2-686x-50y+2375=0

eccentricity

49 x^{2} - 25 y^{2} - 686 x - 50 y + 2375 = 0

\frac{74}{5}

Solution steps

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

Calculate Hyperbola properties

49 x^{2} - 25 y^{2} - 686 x - 50 y + 2375 = 0 :

Right-left Hyperbola with

(h, k) = (7, - 1), a = \frac{1}{7}, b = \frac{1}{5}

= \frac{( \frac{1}{7} ) ^{2} + ( \frac{1}{5} ) ^{2}}{\frac{1}{7}}

Refine

= \frac{74}{5}

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

+ \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

What is the eccentricity 49x^2-25y^2-686x-50y+2375=0 ?
The eccentricity 49x^2-25y^2-686x-50y+2375=0 is (sqrt(74))/5