What is the center 25x^2+9y^2-250x-90y+625=0 ?

The center 25x^2+9y^2-250x-90y+625=0 is (5,5)

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

center

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

(5, 5)

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (5, 5), a = 3, b = 5

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

And the center is:

(5, 5)

\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

\frac{x ^{2}}{4} + \frac{y ^{2}}{9} = 1

8 x^{2} + 2 y^{2} + 16 x = 1

What is the center 25x^2+9y^2-250x-90y+625=0 ?
The center 25x^2+9y^2-250x-90y+625=0 is (5,5)