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

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

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

center

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

(- 3, - 1)

Solution steps

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

Rewrite

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

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

And the center is:

(- 3, - 1)

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

\frac{x ^{2}}{4} + \frac{y ^{2}}{3} = 1

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

x^{2} - 4 x + 9 y^{2} + 54 y + 4 = 0

\frac{( x - 4 ) ^{2}}{100} + \frac{( y + 5 ) ^{2}}{64} = 1

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