What is the center 4x^2+9y^2-16x-18y-11=0 ?

The center 4x^2+9y^2-16x-18y-11=0 is (2,1)

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

center

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

(2, 1)

Solution steps

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

Rewrite

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

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

\frac{( x - 1 ) ^{2}}{100} + \frac{( y - 2 ) ^{2}}{36} = 1

\frac{x ^{2}}{100} + \frac{y ^{2}}{64} = 1

4 x^{2} + 5 y^{2} - 2 x + 78 y - 83 = x - 3 y + 3

135 x^{2} + 256 y^{2} - 34560 = 0

What is the center 4x^2+9y^2-16x-18y-11=0 ?
The center 4x^2+9y^2-16x-18y-11=0 is (2,1)