What is the eccentricity 9x^2+16y^2-54x+64y+1=0 ?

The eccentricity 9x^2+16y^2-54x+64y+1=0 is (sqrt(7))/4

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eccentricity 9x^2+16y^2-54x+64y+1=0

eccentricity

9 x^{2} + 16 y^{2} - 54 x + 64 y + 1 = 0

\frac{7}{4}

Solution steps

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

Calculate ellipse properties

9 x^{2} + 16 y^{2} - 54 x + 64 y + 1 = 0 :

Ellipse with center

(h, k) = (3, - 2), 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} + 9 y^{2} = 36

4 x^{2} + 3 y^{2} - 24 x + 18 y + 51 = 0

\frac{x ^{2}}{36} + \frac{y ^{2}}{49} = 1

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

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

What is the eccentricity 9x^2+16y^2-54x+64y+1=0 ?
The eccentricity 9x^2+16y^2-54x+64y+1=0 is (sqrt(7))/4