What is the center 9x^2+18x+4y^2-24y+9=0 ?

The center 9x^2+18x+4y^2-24y+9=0 is (-1,3)

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center 9x^2+18x+4y^2-24y+9=0

center

9 x^{2} + 18 x + 4 y^{2} - 24 y + 9 = 0

(- 1, 3)

Solution steps

9 x^{2} + 18 x + 4 y^{2} - 24 y + 9 = 0

Rewrite

9 x^{2} + 18 x + 4 y^{2} - 24 y + 9 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

And the center is:

(- 1, 3)

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

4 x^{2} + 9 y^{2} = 144

\frac{( x + 4 ) ^{2}}{16} + \frac{( y - 2 ) ^{2}}{9} = 1

x^{2} - 8 x + 8 y^{2} + 12 y = 0

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

What is the center 9x^2+18x+4y^2-24y+9=0 ?
The center 9x^2+18x+4y^2-24y+9=0 is (-1,3)