What is the eccentricity x^2+42y^2=42 ?

The eccentricity x^2+42y^2=42 is sqrt(41/42)

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eccentricity x^2+42y^2=42

eccentricity

x^{2} + 42 y^{2} = 42

\frac{41}{42}

Solution steps

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

Calculate ellipse properties

x^{2} + 42 y^{2} = 42 :

Ellipse with center

(h, k) = (0, 0), a = 42, b = 1

= \frac{( 42 ) ^{2} - 1 ^{2}}{42}

\frac{( 42 ) ^{2} - 1 ^{2}}{42} = \frac{41}{42}

= \frac{41}{42}

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

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

4 x^{2} + 49 y^{2} = 196

\frac{( x + 4 ) ^{2}}{\frac{25}{4}} + (y - 6)^{2} = 1

7 x^{2} + 9 y^{2} = 63

What is the eccentricity x^2+42y^2=42 ?
The eccentricity x^2+42y^2=42 is sqrt(41/42)