What is the center 25(x+1)^2+9(y-2)^2=225 ?

The center 25(x+1)^2+9(y-2)^2=225 is (-1,2)

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center 25(x+1)^2+9(y-2)^2=225

center

25 (x + 1)^{2} + 9 (y - 2)^{2} = 225

(- 1, 2)

Solution steps

25 (x + 1)^{2} + 9 (y - 2)^{2} = 225

Rewrite

25 (x + 1)^{2} + 9 (y - 2)^{2} = 225

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (- 1, 2), a = 3, b = 5

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- 1, 2), b = 5, a = 3

And the center is:

(- 1, 2)

(\frac{( x - 2 ) ^{2}}{16}) + (\frac{y ^{2}}{9}) = 1

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

36 x^{2} + 5 y^{2} - 90 y - 495 = 0

x^{2} + 4 y^{2} = 36

\frac{( x + 1 ) ^{2}}{16} + \frac{( y - 2 ) ^{2}}{25} = 1

What is the center 25(x+1)^2+9(y-2)^2=225 ?
The center 25(x+1)^2+9(y-2)^2=225 is (-1,2)