What is the center 25(x-2)^2+9(y+3)^2=225 ?

The center 25(x-2)^2+9(y+3)^2=225 is (2,-3)

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center 25(x-2)^2+9(y+3)^2=225

center

25 (x - 2)^{2} + 9 (y + 3)^{2} = 225

(2, - 3)

Solution steps

25 (x - 2)^{2} + 9 (y + 3)^{2} = 225

Rewrite

25 (x - 2)^{2} + 9 (y + 3)^{2} = 225

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (2, - 3), a = 3, b = 5

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (2, - 3), b = 5, a = 3

And the center is:

(2, - 3)

9 x^{2} + 25 y^{2} - 36 x - 50 y + 60 = 0

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

\frac{x ^{2}}{36} + \frac{y ^{2}}{121} = 1

9 x^{2} + 4 y^{2} - 18 x - 16 y - 11 = 0

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

What is the center 25(x-2)^2+9(y+3)^2=225 ?
The center 25(x-2)^2+9(y+3)^2=225 is (2,-3)