What is the eccentricity 4x^2+3y^2-24x+18y+51=0 ?

The eccentricity 4x^2+3y^2-24x+18y+51=0 is 1/2

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

eccentricity

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

\frac{1}{2}

Solution steps

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

Calculate ellipse properties

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

Ellipse with center

(h, k) = (3, - 3), b = 2, a = 3

= \frac{2 ^{2} - ( 3 ) ^{2}}{2}

\frac{2 ^{2} - ( 3 ) ^{2}}{2} = \frac{1}{2}

= \frac{1}{2}

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

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

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

+ 36 x^{2} + y^{2} = 36

(x - 1)^{2} + (y - 2)^{2} = 30

What is the eccentricity 4x^2+3y^2-24x+18y+51=0 ?
The eccentricity 4x^2+3y^2-24x+18y+51=0 is 1/2