What is the eccentricity x^2-y^2-4x-6y-14=0 ?

The eccentricity x^2-y^2-4x-6y-14=0 is square root of 2

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eccentricity x^2-y^2-4x-6y-14=0

eccentricity

x^{2} - y^{2} - 4 x - 6 y - 14 = 0

2

Solution steps

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

Calculate Hyperbola properties

x^{2} - y^{2} - 4 x - 6 y - 14 = 0 :

Right-left Hyperbola with

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

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

Refine

= 2

\frac{x ^{2}}{144} - \frac{y ^{2}}{81} = 1

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

9 x^{2} - 4 y^{2} + 54 x + 16 y + 29 = 0

36 x^{2} - 49 y^{2} = 1

\frac{y ^{2}}{4} - \frac{x ^{2}}{9} = 1

What is the eccentricity x^2-y^2-4x-6y-14=0 ?
The eccentricity x^2-y^2-4x-6y-14=0 is square root of 2