What is the eccentricity 3x^2-4y^2=12 ?

The eccentricity 3x^2-4y^2=12 is (sqrt(7))/2

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eccentricity 3x^2-4y^2=12

eccentricity

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

\frac{7}{2}

Solution steps

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

Calculate Hyperbola properties

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

Right-left Hyperbola with

(h, k) = (0, 0), a = 2, b = 3

= \frac{2 ^{2} + ( 3 ) ^{2}}{2}

Refine

= \frac{7}{2}

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

\frac{x ^{2}}{36} - \frac{y ^{2}}{4} = 1

\frac{x ^{2}}{40} - \frac{y ^{2}}{120} = 1

0 = - \frac{400}{9} x^{2} + 16 y^{2} + 400

\frac{x ^{2}}{121} - \frac{y ^{2}}{81} = 1

What is the eccentricity 3x^2-4y^2=12 ?
The eccentricity 3x^2-4y^2=12 is (sqrt(7))/2