What is ((x+1)^2)/3+((y-1)^2)/6 =4 ?

The solution to ((x+1)^2)/3+((y-1)^2)/6 =4 is Ellipse with (h,k)=(-1,1),a=2sqrt(3),b=2sqrt(6)

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((x+1)^2)/3+((y-1)^2)/6 =4

\frac{( x + 1 ) ^{2}}{3} + \frac{( y - 1 ) ^{2}}{6} = 4

(h, k) = (- 1, 1), a = 23, b = 26

Solution steps

\frac{( x + 1 ) ^{2}}{3} + \frac{( y - 1 ) ^{2}}{6} = 4

Rewrite

\frac{( x + 1 ) ^{2}}{3} + \frac{( y - 1 ) ^{2}}{6} = 4

in the form of the standard ellipse equation

\frac{( x - ( - 1 ) ) ^{2}}{( 2 3 ) ^{2}} + \frac{( y - 1 ) ^{2}}{( 2 6 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 1, 1), a = 23, b = 26

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- 1, 1), b = 26, a = 23

\frac{( x - 4 ) ^{2}}{9} + \frac{( y + 2 ) ^{2}}{25} = 1

\frac{( x ^{(2)} )}{( 16 )} + \frac{( y ^{(2)} )}{( 25 )} = 1

2 x^{2} - 6 < - 6 y^{2}

\frac{x ^{2}}{49} + \frac{y ^{2}}{169} = 1

(- y - 6)^{2} + 8 x^{2} = 64

What is ((x+1)^2)/3+((y-1)^2)/6 =4 ?
The solution to ((x+1)^2)/3+((y-1)^2)/6 =4 is Ellipse with (h,k)=(-1,1),a=2sqrt(3),b=2sqrt(6)