What is the eccentricity 4x^2+9y^2-8x-32=0 ?

The eccentricity 4x^2+9y^2-8x-32=0 is (sqrt(5))/3

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eccentricity 4x^2+9y^2-8x-32=0

eccentricity

4 x^{2} + 9 y^{2} - 8 x - 32 = 0

\frac{5}{3}

Solution steps

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

Calculate ellipse properties

4 x^{2} + 9 y^{2} - 8 x - 32 = 0 :

Ellipse with center

(h, k) = (1, 0), a = 3, b = 2

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

\frac{3 ^{2} - 2 ^{2}}{3} = \frac{5}{3}

= \frac{5}{3}

9 x^{2} + 6 y^{2} = 54

3 x^{2} + 10 y^{2} = 30

x^{2} + 4 y^{2} = 10

\frac{y ^{2}}{16} + \frac{x ^{2}}{9} = 1

2 x^{2} + 8 y^{2} = 16

What is the eccentricity 4x^2+9y^2-8x-32=0 ?
The eccentricity 4x^2+9y^2-8x-32=0 is (sqrt(5))/3