What is the eccentricity 4x^2-9y^2+32x+36y+64=0 ?

The eccentricity 4x^2-9y^2+32x+36y+64=0 is (sqrt(13))/2

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eccentricity 4x^2-9y^2+32x+36y+64=0

eccentricity

4 x^{2} - 9 y^{2} + 32 x + 36 y + 64 = 0

\frac{13}{2}

Solution steps

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

Calculate Hyperbola properties

4 x^{2} - 9 y^{2} + 32 x + 36 y + 64 = 0 :

Up-down Hyperbola with

(h, k) = (- 4, 2), a = 2, b = 3

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

Refine

= \frac{13}{2}

9 x^{2} - 16 y^{2} = 4

\frac{x ^{2}}{27} - \frac{y ^{2}}{360} = 1

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

\frac{x ^{2}}{49} - \frac{y ^{2}}{4} = 1

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

What is the eccentricity 4x^2-9y^2+32x+36y+64=0 ?
The eccentricity 4x^2-9y^2+32x+36y+64=0 is (sqrt(13))/2