What is the center 9x^2+4y^2-18x+8y-23=0 ?

The center 9x^2+4y^2-18x+8y-23=0 is (1,-1)

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center 9x^2+4y^2-18x+8y-23=0

center

9 x^{2} + 4 y^{2} - 18 x + 8 y - 23 = 0

(1, - 1)

Solution steps

9 x^{2} + 4 y^{2} - 18 x + 8 y - 23 = 0

Rewrite

9 x^{2} + 4 y^{2} - 18 x + 8 y - 23 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

And the center is:

(1, - 1)

\frac{x ^{2}}{9} + \frac{y ^{2}}{36} = 1

25 x^{2} + 9 y^{2} - 250 x - 90 y + 625 = 0

\frac{( x + 2 ) ^{2}}{16} + \frac{y ^{2}}{49} = 1

\frac{( x + 1 ) ^{2}}{9} + \frac{( y + 3 ) ^{2}}{16} = 1

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

What is the center 9x^2+4y^2-18x+8y-23=0 ?
The center 9x^2+4y^2-18x+8y-23=0 is (1,-1)