What is the eccentricity ((x-3)^2)/2+((y-4)^2)/4 =1 ?

The eccentricity ((x-3)^2)/2+((y-4)^2)/4 =1 is 1/(sqrt(2))

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eccentricity ((x-3)^2)/2+((y-4)^2)/4 =1

eccentricity

\frac{( x - 3 ) ^{2}}{2} + \frac{( y - 4 ) ^{2}}{4} = 1

\frac{1}{2}

Solution steps

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

Calculate ellipse properties

\frac{( x - 3 ) ^{2}}{2} + \frac{( y - 4 ) ^{2}}{4} = 1 :

Ellipse with center

(h, k) = (3, 4), b = 2, a = 2

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

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

= \frac{1}{2}

8 x^{2} + 4 y^{2} + 16 x - 12 y - 15 = 0

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

\frac{x ^{2}}{8 ^{2}} + \frac{y ^{2}}{3 ^{2}} = 1

16 x^{2} + 4 y^{2} + 96 x - 24 y + 116 = 0

x^{2} + 4 y^{2} - 4 x - 8 y - 92 = 0

What is the eccentricity ((x-3)^2)/2+((y-4)^2)/4 =1 ?
The eccentricity ((x-3)^2)/2+((y-4)^2)/4 =1 is 1/(sqrt(2))