What is the center 19x^2+y^2=38 ?

The center 19x^2+y^2=38 is (0,0)

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center 19x^2+y^2=38

center

19 x^{2} + y^{2} = 38

(0, 0)

Solution steps

19 x^{2} + y^{2} = 38

Rewrite

19 x^{2} + y^{2} = 38

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( 2 ) ^{2}} + \frac{( y - 0 ) ^{2}}{( 38 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = 2, b = 38

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 0), b = 38, a = 2

And the center is:

(0, 0)

x^{2} + y^{2} + 10 y = 0

36 x^{2} + 9 y^{2} + 36 y - 288 = 0

\frac{( x - 3 ) ^{2}}{25} + \frac{( y + 2 ) ^{2}}{16} = 1

x^{2} + 7 x + 3 y^{2} + y = 0

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