What is the center 5x^2+2y^2=50 ?

The center 5x^2+2y^2=50 is (0,0)

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center 5x^2+2y^2=50

center

5 x^{2} + 2 y^{2} = 50

(0, 0)

Solution steps

5 x^{2} + 2 y^{2} = 50

Rewrite

5 x^{2} + 2 y^{2} = 50

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( 10 ) ^{2}} + \frac{( y - 0 ) ^{2}}{5 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = 10, b = 5

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 0), b = 5, a = 10

And the center is:

(0, 0)

\frac{x ^{2}}{63500} + \frac{y ^{2}}{50900} = 1

\frac{x ^{2}}{a ^{2}} + \frac{y ^{2}}{b ^{2}} = 1

x^{2} + \frac{y ^{2}}{16} = 1

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

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