What is ((x-1)^2)/9+((y+1)^2)/4 =1 ?

The solution to ((x-1)^2)/9+((y+1)^2)/4 =1 is Ellipse with (h,k)=(1,-1),a=3,b=2

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((x-1)^2)/9+((y+1)^2)/4 =1

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

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

Solution steps

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

Rewrite

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

4 x^{2} + 9 y^{2} + 8 x - 36 y + 4 = 0

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

x^{2} - 2 x + \frac{y ^{2}}{4} - y = 14

\frac{( x + 1 ) ^{2}}{28} + \frac{( y + 5 ) ^{2}}{23} = 1

2 x^{2} + y^{2} + 12 x - 2 y + 17 = 0

What is ((x-1)^2)/9+((y+1)^2)/4 =1 ?
The solution to ((x-1)^2)/9+((y+1)^2)/4 =1 is Ellipse with (h,k)=(1,-1),a=3,b=2