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

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

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

center

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

(3, - 2)

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

And the center is:

(3, - 2)

x^{2} + 3 y^{2} + 2 x - 12 y + 10 = 0

\frac{x ^{2}}{16} + \frac{( y + 1 ) ^{2}}{4} - 1 = 0

3 x^{2} + 3 y^{2} - 12 y = 0

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

4 y^{2} + 2 x^{2} - 4 y - 8 x - 15 = 0

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