What is the axis x^2+4y^2=1 ?

The axis x^2+4y^2=1 is semi-major axis a=1, semi-minor axis b= 1/2

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axis x^2+4y^2=1

axis

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

semi - major axis a = 1, semi - minor axis b = \frac{1}{2}

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 0), a = 1, b = \frac{1}{2}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = 1, b = \frac{1}{2}

\frac{( x - 2 ) ^{2}}{4} + \frac{( y + 2 ) ^{2}}{9} = 1

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

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

5 x^{2} + 9 y^{2} - 10 x - 36 y = 4

x^{2} + 4 y^{2} - 6 x - 16 y = 36

What is the axis x^2+4y^2=1 ?
The axis x^2+4y^2=1 is semi-major axis a=1, semi-minor axis b= 1/2