What is the eccentricity 2y^2-4x^2=1 ?

The eccentricity 2y^2-4x^2=1 is sqrt(3/2)

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eccentricity 2y^2-4x^2=1

eccentricity

2 y^{2} - 4 x^{2} = 1

\frac{3}{2}

Solution steps

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

Calculate Hyperbola properties

2 y^{2} - 4 x^{2} = 1 :

Up-down Hyperbola with

(h, k) = (0, 0), a = \frac{1}{2}, b = \frac{1}{2}

= \frac{( \frac{1}{2} ) ^{2} + ( \frac{1}{2} ) ^{2}}{\frac{1}{2}}

Refine

= \frac{3}{2}

\frac{x ^{2}}{27} - \frac{y ^{2}}{72} = 1

\frac{x ^{2}}{36} - \frac{y ^{2}}{9} = 1

25 x^{2} - 36 y^{2} = 900

\frac{x ^{2}}{16} - \frac{y ^{2}}{81} = 1

9 x^{2} - 9 y^{2} = 9

What is the eccentricity 2y^2-4x^2=1 ?
The eccentricity 2y^2-4x^2=1 is sqrt(3/2)