What is the eccentricity 4x^2+32x+25y^2-250y+589=0 ?

The eccentricity 4x^2+32x+25y^2-250y+589=0 is (sqrt(21))/5

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eccentricity 4x^2+32x+25y^2-250y+589=0

eccentricity

4 x^{2} + 32 x + 25 y^{2} - 250 y + 589 = 0

\frac{21}{5}

Solution steps

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

Calculate ellipse properties

4 x^{2} + 32 x + 25 y^{2} - 250 y + 589 = 0 :

Ellipse with center

(h, k) = (- 4, 5), a = 5, b = 2

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

\frac{5 ^{2} - 2 ^{2}}{5} = \frac{21}{5}

= \frac{21}{5}

\frac{x ^{2}}{9} + \frac{( y + 5 ) ^{2}}{25} = 1

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

2 x^{2} + 3 y^{2} + 4 x = 1

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

25 x^{2} + 16 y^{2} + 100 x - 96 y - 156 = 0

What is the eccentricity 4x^2+32x+25y^2-250y+589=0 ?
The eccentricity 4x^2+32x+25y^2-250y+589=0 is (sqrt(21))/5