What is ((x-3)^2)/9+((y+1)^2)/4 =1 ?

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

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((x-3)^2)/9+((y+1)^2)/4 =1

\frac{( x - 3 ) ^{2}}{9} + \frac{( y + 1 ) ^{2}}{4} = 1

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

Solution steps

\frac{( x - 3 ) ^{2}}{9} + \frac{( y + 1 ) ^{2}}{4} = 1

Rewrite

\frac{( x - 3 ) ^{2}}{9} + \frac{( y + 1 ) ^{2}}{4} = 1

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

\frac{( x - 1 ) ^{2}}{9} + \frac{( y + 3 ) ^{2}}{25} = 1

\frac{x ^{2}}{81} + \frac{y ^{2}}{36} = 1

x^{2} + 25 y^{2} - 200 y + 375 = 0

\frac{( x + 1 ) ^{2}}{36} + \frac{( y + 3 ) ^{2}}{25} = 1

x^{2} + 9 y^{2} + 2 x - 18 y + 1 = 0

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