What is the eccentricity 16x^2-9y^2+32x+72y-704=0 ?

The eccentricity 16x^2-9y^2+32x+72y-704=0 is 5/3

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eccentricity 16x^2-9y^2+32x+72y-704=0

eccentricity

16 x^{2} - 9 y^{2} + 32 x + 72 y - 704 = 0

\frac{5}{3}

Solution steps

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

Calculate Hyperbola properties

16 x^{2} - 9 y^{2} + 32 x + 72 y - 704 = 0 :

Right-left Hyperbola with

(h, k) = (- 1, 4), a = 6, b = 8

= \frac{6 ^{2} + 8 ^{2}}{6}

Refine

= \frac{5}{3}

16 y^{2} - 32 y - 9 x^{2} - 18 x = 137

\frac{x ^{2}}{a ^{2}} - \frac{y ^{2}}{b ^{2}} = 1

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

3 x^{2} - 4 y^{2} = 12

4 y^{2} - 9 x^{2} + 8 y - 54 x - 113 = 0

What is the eccentricity 16x^2-9y^2+32x+72y-704=0 ?
The eccentricity 16x^2-9y^2+32x+72y-704=0 is 5/3