What is the eccentricity 25x^2+9y^2-150x-18y+9=0 ?

The eccentricity 25x^2+9y^2-150x-18y+9=0 is 4/5

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eccentricity 25x^2+9y^2-150x-18y+9=0

eccentricity

25 x^{2} + 9 y^{2} - 150 x - 18 y + 9 = 0

\frac{4}{5}

Solution steps

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

Calculate ellipse properties

25 x^{2} + 9 y^{2} - 150 x - 18 y + 9 = 0 :

Ellipse with center

(h, k) = (3, 1), b = 5, a = 3

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

\frac{5 ^{2} - 3 ^{2}}{5} = \frac{4}{5}

= \frac{4}{5}

\frac{x ^{2}}{169} + \frac{y ^{2}}{144} = 1

\frac{( x - 4 ) ^{2}}{3} + \frac{y ^{2}}{3} = 1

9 x^{2} + 16 y^{2} - 36 x + 96 y + 36 = 0

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

\frac{x ^{2}}{9} + \frac{y ^{2}}{49} = 1

What is the eccentricity 25x^2+9y^2-150x-18y+9=0 ?
The eccentricity 25x^2+9y^2-150x-18y+9=0 is 4/5