What is the eccentricity 16x^2+192x+576+25y^2=1600 ?

The eccentricity 16x^2+192x+576+25y^2=1600 is 3/5

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eccentricity 16x^2+192x+576+25y^2=1600

eccentricity

16 x^{2} + 192 x + 576 + 25 y^{2} = 1600

\frac{3}{5}

Solution steps

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

Calculate ellipse properties

16 x^{2} + 192 x + 576 + 25 y^{2} = 1600 :

Ellipse with center

(h, k) = (- 6, 0), a = 10, b = 8

= \frac{1 0 ^{2} - 8 ^{2}}{10}

\frac{1 0 ^{2} - 8 ^{2}}{10} = \frac{3}{5}

= \frac{3}{5}

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

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

4 x^{2} + 9 y^{2} = 144

\frac{x ^{2}}{16} + \frac{y ^{2}}{81} = 1

(y + 2)^{2} = 1 - 2 (x + 1)^{2}

What is the eccentricity 16x^2+192x+576+25y^2=1600 ?
The eccentricity 16x^2+192x+576+25y^2=1600 is 3/5