What is the center 4x^2+25y^2=100 ?

The center 4x^2+25y^2=100 is (0,0)

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center 4x^2+25y^2=100

center

4 x^{2} + 25 y^{2} = 100

(0, 0)

Solution steps

4 x^{2} + 25 y^{2} = 100

Rewrite

4 x^{2} + 25 y^{2} = 100

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 0), a = 5, b = 2

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = 5, b = 2

And the center is:

(0, 0)

2 (x + \frac{1}{4})^{2} + y^{2} = 8

x^{2} + 4 y^{2} = 16

\frac{x ^{2}}{144} + \frac{y ^{2}}{169} = 1

4 x^{2} + y^{2} = 1

16 x^{2} + y^{2} = 16