What is the center 9x^2+4y^2+36x-24y+36=0 ?

The center 9x^2+4y^2+36x-24y+36=0 is (-2,3)

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center 9x^2+4y^2+36x-24y+36=0

center

9 x^{2} + 4 y^{2} + 36 x - 24 y + 36 = 0

(- 2, 3)

Solution steps

9 x^{2} + 4 y^{2} + 36 x - 24 y + 36 = 0

Rewrite

9 x^{2} + 4 y^{2} + 36 x - 24 y + 36 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

And the center is:

(- 2, 3)

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

\frac{x ^{2}}{169} + \frac{y ^{2}}{25} = 1

\frac{x ^{2}}{16} - \frac{y ^{2}}{36} = 1

\frac{x ^{2}}{16} + \frac{y ^{2}}{25} = 1

y^{2} - 6 y - 4 x + 5 = 0

What is the center 9x^2+4y^2+36x-24y+36=0 ?
The center 9x^2+4y^2+36x-24y+36=0 is (-2,3)