What is the center 25x^2-200x+y^2+4y+379=0 ?

The center 25x^2-200x+y^2+4y+379=0 is (4,-2)

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center 25x^2-200x+y^2+4y+379=0

center

25 x^{2} - 200 x + y^{2} + 4 y + 379 = 0

(4, - 2)

Solution steps

25 x^{2} - 200 x + y^{2} + 4 y + 379 = 0

Rewrite

25 x^{2} - 200 x + y^{2} + 4 y + 379 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (4, - 2), a = 1, b = 5

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (4, - 2), b = 5, a = 1

And the center is:

(4, - 2)

4 x^{2} + 9 y^{2} - 24 x + 72 y + 144 = 0

4 x^{2} + y^{2} + 8 x - 4 y + 4 = 0

\frac{x ^{2}}{64} + \frac{y ^{2}}{36} = 1

\frac{x ^{2}}{25} + \frac{y ^{2}}{9} = 1

x^{2} + 4 y^{2} - 6 x + 8 y + 9 = 0

What is the center 25x^2-200x+y^2+4y+379=0 ?
The center 25x^2-200x+y^2+4y+379=0 is (4,-2)