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

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

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

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

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

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

16 x^{2} + 4 y^{2} + 16 x + 49 y - 81 = 0

\frac{( x - 4 ) ^{2}}{10} + \frac{( y - 2 ) ^{2}}{6} = 1

9 x^{2} - 18 x + 4 y^{2} - 27 = 0

4 x^{2} + 25 y^{2} + 8 x = 96

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

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