What is the eccentricity 4x^2+9y^2-8x-36y+4=0 ?

The eccentricity 4x^2+9y^2-8x-36y+4=0 is (sqrt(5))/3

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eccentricity 4x^2+9y^2-8x-36y+4=0

eccentricity

4 x^{2} + 9 y^{2} - 8 x - 36 y + 4 = 0

\frac{5}{3}

Solution steps

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

Calculate ellipse properties

4 x^{2} + 9 y^{2} - 8 x - 36 y + 4 = 0 :

Ellipse with center

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

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

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

= \frac{5}{3}

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

9 x^{2} + 36 y^{2} = 324

5 x^{2} + 7 y^{2} = 35

3 x^{2} + y^{2} + 18 x - 2 y - 8 = 0

x^{2} + 4 y^{2} - 16 = 0

What is the eccentricity 4x^2+9y^2-8x-36y+4=0 ?
The eccentricity 4x^2+9y^2-8x-36y+4=0 is (sqrt(5))/3