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

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

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

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

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

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

16 x^{2} - 64 x + 25 y^{2} + 150 y + 189 = 0

2 x^{2} + 3 y^{2} = 12

x^{2} + 4 y^{2} \leq 4

2 x^{2} + 4 y^{2} + 10 x + 9 y - 5 = 0

\frac{( y - 6 ) ^{2}}{36} + \frac{( x + 3 ) ^{2}}{16} = 1

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