What is the eccentricity 16x^2-9y^2+96x-72y+144=0 ?

The eccentricity 16x^2-9y^2+96x-72y+144=0 is 5/4

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

eccentricity

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

\frac{5}{4}

Solution steps

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

Calculate Hyperbola properties

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

Up-down Hyperbola with

(h, k) = (- 3, - 4), a = 4, b = 3

= \frac{4 ^{2} + 3 ^{2}}{4}

Refine

= \frac{5}{4}

\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

\frac{x ^{2}}{27} - \frac{y ^{2}}{360} = 1

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

What is the eccentricity 16x^2-9y^2+96x-72y+144=0 ?
The eccentricity 16x^2-9y^2+96x-72y+144=0 is 5/4