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

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

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

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

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

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

4 x^{2} + y^{2} + 6 y + 5 = 0

\frac{x ^{2}}{5 ^{2}} + \frac{y ^{2}}{7 ^{2}} = 1

9 x^{2} - 18 x + 4 y^{2} + 16 y - 11 = 0

3 x^{2} + 5 y^{2} - 6 = 0

16 x^{2} + 25 y^{2} - 48 x + 100 y - 264 = 0

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