What is the center 9x^2+25y^2+108x-200y+499=0 ?

The center 9x^2+25y^2+108x-200y+499=0 is (-6,4)

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center 9x^2+25y^2+108x-200y+499=0

center

(- 6, 4)

Solution steps

9 x^{2} + 25 y^{2} + 108 x - 200 y + 499 = 0

Rewrite

9 x^{2} + 25 y^{2} + 108 x - 200 y + 499 = 0

in the form of the standard ellipse equation

\frac{( x - ( - 6 ) ) ^{2}}{5 ^{2}} + \frac{( y - 4 ) ^{2}}{3 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 6, 4), a = 5, b = 3

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 6, 4), a = 5, b = 3

And the center is:

(- 6, 4)

What is the center 9x^2+25y^2+108x-200y+499=0 ?
The center 9x^2+25y^2+108x-200y+499=0 is (-6,4)