What is the center 4x^2+25y^2-32x+200y+364=0 ?

The center 4x^2+25y^2-32x+200y+364=0 is (4,-4)

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center 4x^2+25y^2-32x+200y+364=0

center

4 x^{2} + 25 y^{2} - 32 x + 200 y + 364 = 0

(4, - 4)

Solution steps

4 x^{2} + 25 y^{2} - 32 x + 200 y + 364 = 0

Rewrite

4 x^{2} + 25 y^{2} - 32 x + 200 y + 364 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (4, - 4), a = 5, b = 2

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (4, - 4), a = 5, b = 2

And the center is:

(4, - 4)

(x 3)^{2} + (y + 4)^{2} = 25

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

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

\frac{( x + 1 ) ^{2}}{25} + \frac{( y - 4 ) ^{2}}{169} = 1

4 x^{2} + 7 y^{2} < 28

What is the center 4x^2+25y^2-32x+200y+364=0 ?
The center 4x^2+25y^2-32x+200y+364=0 is (4,-4)