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(b^2+a^2))/b

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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{b ^{2} + a ^{2}}{b}

Solution steps

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

Calculate Hyperbola properties

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

Up-down Hyperbola with

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

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

\frac{y ^{2}}{64} - \frac{x ^{2}}{36} = 1

\frac{x ^{2}}{9} - \frac{y ^{2}}{25} = 1

\frac{y ^{2}}{25} - \frac{x ^{2}}{16} = 1

\frac{( x + 1 ) ^{2}}{4} - (y - 5)^{2} = 4

9 x^{2} - 16 y^{2} = 144

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(b^2+a^2))/b