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

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

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

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

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

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

4 = x^{2} + 2 y^{2}

\frac{( x + 1 ) ^{2}}{64} + \frac{( y - 1 ) ^{2}}{100} = 1

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

\frac{x ^{2}}{24} + \frac{y ^{2}}{20} = 1

16 (x^{2}) + 9 (y^{2}) - 144 = 0

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