What is the eccentricity x^2-4y^2-2x+16y=20 ?

The eccentricity x^2-4y^2-2x+16y=20 is (sqrt(5))/2

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eccentricity x^2-4y^2-2x+16y=20

eccentricity

x^{2} - 4 y^{2} - 2 x + 16 y = 20

\frac{5}{2}

Solution steps

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

Calculate Hyperbola properties

x^{2} - 4 y^{2} - 2 x + 16 y = 20 :

Right-left Hyperbola with

(h, k) = (1, 2), a = 5, b = \frac{5}{2}

= \frac{( 5 ) ^{2} + ( \frac{5}{2} ) ^{2}}{5}

Refine

= \frac{5}{2}

5 y^{2} - 16 x^{2} + 400 = 0

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

\frac{x ^{2}}{25} - \frac{y ^{2}}{36} = 1

x^{2} - 4 y^{2} - 4 x + 8 y - 16 = 0

\frac{( x - 2 ) ^{2}}{5} - \frac{( y + 1 ) ^{2}}{9} = 1

What is the eccentricity x^2-4y^2-2x+16y=20 ?
The eccentricity x^2-4y^2-2x+16y=20 is (sqrt(5))/2