What is the eccentricity 9x^2+16y^2-144=0 ?

The eccentricity 9x^2+16y^2-144=0 is (sqrt(7))/4

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eccentricity 9x^2+16y^2-144=0

eccentricity

9 x^{2} + 16 y^{2} - 144 = 0

\frac{7}{4}

Solution steps

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

Calculate ellipse properties

9 x^{2} + 16 y^{2} - 144 = 0 :

Ellipse with center

(h, k) = (0, 0), a = 4, b = 3

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

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

= \frac{7}{4}

\frac{x ^{2}}{36} + \frac{y ^{2}}{16} = 1

4 x^{2} + 9 y^{2} - 16 x + 18 y = 11

4 x^{2} + 3 y^{2} - 8 x + 18 y + 19 = 0

x^{2} + 4 y^{2} - 6 x + 20 y - 2 = 0

\frac{x ^{2}}{25} + \frac{( y + 3 ) ^{2}}{49} = 1

What is the eccentricity 9x^2+16y^2-144=0 ?
The eccentricity 9x^2+16y^2-144=0 is (sqrt(7))/4