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

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

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

center

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

(1, 2)

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

And the center is:

(1, 2)

\frac{( x + 5 ) ^{2}}{5} + \frac{( y + 9 ) ^{2}}{9} = 1

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

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

4 x^{2} + 9 y^{2} = 144

\frac{( x + 4 ) ^{2}}{16} + \frac{( y - 2 ) ^{2}}{9} = 1

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