What is (x^2)/9+(2x)/9+y^2-6y+9=0 ?

The solution to (x^2)/9+(2x)/9+y^2-6y+9=0 is Ellipse with (h,k)=(-1,3),a=1,b= 1/3

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(x^2)/9+(2x)/9+y^2-6y+9=0

\frac{x ^{2}}{9} + \frac{2 x}{9} + y^{2} - 6 y + 9 = 0

(h, k) = (- 1, 3), a = 1, b = \frac{1}{3}

Solution steps

\frac{x ^{2}}{9} + \frac{2 x}{9} + y^{2} - 6 y + 9 = 0

Rewrite

\frac{x ^{2}}{9} + \frac{2 x}{9} + y^{2} - 6 y + 9 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (- 1, 3), a = 1, b = \frac{1}{3}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 1, 3), a = 1, b = \frac{1}{3}

5 x^{2} + 2 y^{2} = 45

\frac{( x + 3 ) ^{2}}{12} + \frac{( y - 2 ) ^{2}}{16} = 1

2 x^{2} + y^{2} - 2 x + 3 y = 5

\frac{x ^{2}}{81} + \frac{y ^{2}}{100} = 1

25 (x + 1)^{2} + 16 (y - 3)^{2} = 400

What is (x^2)/9+(2x)/9+y^2-6y+9=0 ?
The solution to (x^2)/9+(2x)/9+y^2-6y+9=0 is Ellipse with (h,k)=(-1,3),a=1,b= 1/3