What is the center 25x^2+9y^2-150x-18y+9=0 ?

The center 25x^2+9y^2-150x-18y+9=0 is (3,1)

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center 25x^2+9y^2-150x-18y+9=0

center

25 x^{2} + 9 y^{2} - 150 x - 18 y + 9 = 0

(3, 1)

Solution steps

25 x^{2} + 9 y^{2} - 150 x - 18 y + 9 = 0

Rewrite

25 x^{2} + 9 y^{2} - 150 x - 18 y + 9 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (3, 1), a = 3, b = 5

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (3, 1), b = 5, a = 3

And the center is:

(3, 1)

\frac{( x + 2 ) ^{2}}{25} + \frac{( y - 4 ) ^{2}}{4} = 1

4 x^{2} + y^{2} - 48 x + 4 y + 48 = 0

\frac{x ^{2}}{64} + \frac{y ^{2}}{16} = 1

9 (x - 1)^{2} + 4 y^{2} = 36

9 x^{2} + 25 y^{2} + 18 x + 150 y + 9 = 0

What is the center 25x^2+9y^2-150x-18y+9=0 ?
The center 25x^2+9y^2-150x-18y+9=0 is (3,1)