What is the center 9x^2+16y^2=576 ?

The center 9x^2+16y^2=576 is (0,0)

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center 9x^2+16y^2=576

center

9 x^{2} + 16 y^{2} = 576

(0, 0)

Solution steps

9 x^{2} + 16 y^{2} = 576

Rewrite

9 x^{2} + 16 y^{2} = 576

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{8 ^{2}} + \frac{( y - 0 ) ^{2}}{6 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = 8, b = 6

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = 8, b = 6

And the center is:

(0, 0)

\frac{( x - 10 ) ^{2}}{4} + \frac{y ^{2}}{16} = 1

12 x^{2} + 8 x + 8 y^{2} + 12 y = 0

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

25 x^{2} + 16 y^{2} + 100 x - 96 y = 156

16 y^{2} + 25 x^{2} - 80 x + 36 y + 80 = 0