What is the eccentricity 9x^2+16y^2-72x+64y-368=0 ?

The eccentricity 9x^2+16y^2-72x+64y-368=0 is (sqrt(7))/4

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eccentricity 9x^2+16y^2-72x+64y-368=0

eccentricity

9 x^{2} + 16 y^{2} - 72 x + 64 y - 368 = 0

\frac{7}{4}

Solution steps

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

Calculate ellipse properties

9 x^{2} + 16 y^{2} - 72 x + 64 y - 368 = 0 :

Ellipse with center

(h, k) = (4, - 2), a = 8, b = 6

= \frac{8 ^{2} - 6 ^{2}}{8}

\frac{8 ^{2} - 6 ^{2}}{8} = \frac{7}{4}

= \frac{7}{4}

y^{2} = - 16 x

y^{2} = - 16 x

\frac{x ^{2}}{9} - \frac{y ^{2}}{4} = 1

f (x) = - 3 x^{2} + 12 x - 8

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

What is the eccentricity 9x^2+16y^2-72x+64y-368=0 ?
The eccentricity 9x^2+16y^2-72x+64y-368=0 is (sqrt(7))/4