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

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

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

eccentricity

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

\frac{7}{4}

Solution steps

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

Calculate ellipse properties

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

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}

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

4 x^{2} - 16 x + 3 y^{2} + 24 y + 52 = 0

x^{2} + 8 y^{2} = 32

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

3 x^{2} + 2 y^{2} + 6 x - 4 y + 5 = 18

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