What is ((x-2)^2}{1^2}+\frac{(y+1)^2)/2 =1 ?

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

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

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

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

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

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

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

\frac{( x + 3 ) ^{2}}{6 ^{2}} + \frac{( y + 7 ) ^{2}}{2 ^{2}} = 1

25 x^{(2)} - 200 x + y^{(2)} + 4 y + 379 = 0

\frac{( x - 0 ) ^{2}}{2 ^{2}} + \frac{( y - 0 ) ^{2}}{4 ^{2}} = 1

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