What is the center+4x^2+9y^2-16x+18y=11 ?

The center+4x^2+9y^2-16x+18y=11 is (2,-1)

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center+4x^2+9y^2-16x+18y=11

center

+ 4 x^{2} + 9 y^{2} - 16 x + 18 y = 11

(2, - 1)

Solution steps

4 x^{2} + 9 y^{2} - 16 x + 18 y = 11

Rewrite

+ 4 x^{2} + 9 y^{2} - 16 x + 18 y = 11

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

And the center is:

(2, - 1)

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

8 x^{2} + 2 y^{2} + 16 x = 1

25 x^{2} + 16 y^{2} + 50 x - 64 y - 311 = 0

4 x^{2} + 9 y^{2} - 16 x - 18 y - 11 = 0

\frac{( x - 7 ) ^{2}}{25} + \frac{( y - 6 ) ^{2}}{39} = 1

What is the center+4x^2+9y^2-16x+18y=11 ?
The center+4x^2+9y^2-16x+18y=11 is (2,-1)