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

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

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eccentricity (y+2)^2=1-2(x+1)^2

eccentricity

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

\frac{1}{2}

Solution steps

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

Calculate ellipse properties

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

Ellipse with center

(h, k) = (- 1, - 2), b = 1, a = \frac{1}{2}

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

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

= \frac{1}{2}

\frac{x ^{2}}{5} + \frac{y ^{2}}{8} = 1

18 x^{2} + 4 y^{2} - 72 x + 4 y + 37 = 0

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

\frac{x ^{2}}{12} + \frac{y ^{2}}{49} = 1

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

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