What is the axis x^2+2y^2-8y=0 ?

The axis x^2+2y^2-8y=0 is semi-major axis a=2sqrt(2), semi-minor axis b=2

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axis x^2+2y^2-8y=0

axis

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

semi - major axis a = 22, semi - minor axis b = 2

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 2), a = 22, b = 2

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 2), a = 22, b = 2

\frac{x ^{2}}{36} + \frac{y ^{2}}{25} = 1

\frac{x ^{2}}{4 ^{2}} + \frac{y ^{2}}{3 ^{2}} = 1

81 x^{2} - 1296 x + 16 y^{2} + 64 y = - 3952

4 x^{2} + 9 y^{2} + 32 x - 18 y + 37 = 0

\frac{( x + 5 ) ^{2}}{25} + \frac{( y - 5 ) ^{2}}{16} = 1

What is the axis x^2+2y^2-8y=0 ?
The axis x^2+2y^2-8y=0 is semi-major axis a=2sqrt(2), semi-minor axis b=2