What is the eccentricity (x^2)/(a^2)-(y^2)/(b^2)=1 ?

The eccentricity (x^2)/(a^2)-(y^2)/(b^2)=1 is (sqrt(a^2+b^2))/a

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eccentricity (x^2)/(a^2)-(y^2)/(b^2)=1

eccentricity

\frac{x ^{2}}{a ^{2}} - \frac{y ^{2}}{b ^{2}} = 1

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

Solution steps

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

Calculate Hyperbola properties

\frac{x ^{2}}{a ^{2}} - \frac{y ^{2}}{b ^{2}} = 1 :

Right-left Hyperbola with

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

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

\frac{y ^{2}}{4} - (x + 1)^{2} = 1

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

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

What is the eccentricity (x^2)/(a^2)-(y^2)/(b^2)=1 ?
The eccentricity (x^2)/(a^2)-(y^2)/(b^2)=1 is (sqrt(a^2+b^2))/a