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

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

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

eccentricity

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

\frac{3}{2}

Solution steps

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

Calculate ellipse properties

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

Ellipse with center

(h, k) = (- 3, - 1), a = 2, b = 1

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

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

= \frac{3}{2}

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

4 xx + 9 yy = 36

25 x^{2} - 12 y + y^{2} - 26 y = - 11

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