What is the eccentricity 16x^2-9y^2-64x-18y+199=0 ?

The eccentricity 16x^2-9y^2-64x-18y+199=0 is 5/4

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eccentricity 16x^2-9y^2-64x-18y+199=0

eccentricity

16 x^{2} - 9 y^{2} - 64 x - 18 y + 199 = 0

\frac{5}{4}

Solution steps

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

Calculate Hyperbola properties

16 x^{2} - 9 y^{2} - 64 x - 18 y + 199 = 0 :

Up-down Hyperbola with

(h, k) = (2, - 1), a = 4, b = 3

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

Refine

= \frac{5}{4}

\frac{x ^{2}}{4} - \frac{y ^{2}}{16} = 1

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

\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

What is the eccentricity 16x^2-9y^2-64x-18y+199=0 ?
The eccentricity 16x^2-9y^2-64x-18y+199=0 is 5/4