What is the eccentricity 4x^2+25y^2-40x+150y+225=0 ?

The eccentricity 4x^2+25y^2-40x+150y+225=0 is (sqrt(21))/5

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eccentricity 4x^2+25y^2-40x+150y+225=0

eccentricity

4 x^{2} + 25 y^{2} - 40 x + 150 y + 225 = 0

\frac{21}{5}

Solution steps

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

Calculate ellipse properties

4 x^{2} + 25 y^{2} - 40 x + 150 y + 225 = 0 :

Ellipse with center

(h, k) = (5, - 3), 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 ^{2}}{49} = 1

\frac{x ^{2}}{100} + \frac{y ^{2}}{36} = 1

3 x^{2} - 6 x + y^{2} + 4 y - 11 = 0

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

\frac{x ^{2}}{16} + (y - 4)^{2} = 1

What is the eccentricity 4x^2+25y^2-40x+150y+225=0 ?
The eccentricity 4x^2+25y^2-40x+150y+225=0 is (sqrt(21))/5