What is the eccentricity-9x^2+8y^2+36x+48y=36 ?

The eccentricity-9x^2+8y^2+36x+48y=36 is (sqrt(17))/3

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eccentricity-9x^2+8y^2+36x+48y=36

eccentricity

- 9 x^{2} + 8 y^{2} + 36 x + 48 y = 36

\frac{17}{3}

Solution steps

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

Calculate Hyperbola properties

- 9 x^{2} + 8 y^{2} + 36 x + 48 y = 36 :

Up-down Hyperbola with

(h, k) = (2, - 3), a = 3, b = 22

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

Refine

= \frac{17}{3}

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

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

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

- 9 x^{2} + y^{2} - 72 x - 153 = 0

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

What is the eccentricity-9x^2+8y^2+36x+48y=36 ?
The eccentricity-9x^2+8y^2+36x+48y=36 is (sqrt(17))/3