What is the eccentricity 9x^2+16y^2-36x+96y+36=0 ?

The eccentricity 9x^2+16y^2-36x+96y+36=0 is (sqrt(7))/4

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

eccentricity

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

\frac{7}{4}

Solution steps

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

Calculate ellipse properties

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

Ellipse with center

(h, k) = (2, - 3), a = 4, b = 3

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

\frac{4 ^{2} - 3 ^{2}}{4} = \frac{7}{4}

= \frac{7}{4}

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

\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

What is the eccentricity 9x^2+16y^2-36x+96y+36=0 ?
The eccentricity 9x^2+16y^2-36x+96y+36=0 is (sqrt(7))/4