What is the axis x^2+2y^2-2x+8y+5=0 ?

The axis x^2+2y^2-2x+8y+5=0 is semi-major axis a=2, semi-minor axis b=sqrt(2)

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axis x^2+2y^2-2x+8y+5=0

axis

x^{2} + 2 y^{2} - 2 x + 8 y + 5 = 0

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

Solution steps

x^{2} + 2 y^{2} - 2 x + 8 y + 5 = 0

Rewrite

x^{2} + 2 y^{2} - 2 x + 8 y + 5 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (1, - 2), a = 2, b = 2

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (1, - 2), a = 2, b = 2

4 x^{2} + 8 y^{2} - 16 \cdot + 32 y + 32 = 0

16 x^{2} + 9 y^{2} - 128 x - 18 y + 121 = 0

\frac{( x - 30 ) ^{2}}{4 0 ^{2}} + \frac{y ^{2}}{2 ^{2}} = 1

\frac{( x - 2 ) ^{2}}{9} + \frac{( y - 1 ) ^{2}}{25} = 1

4 x^{2} + y^{2} + 16 x + 4 y + 4 = 0

What is the axis x^2+2y^2-2x+8y+5=0 ?
The axis x^2+2y^2-2x+8y+5=0 is semi-major axis a=2, semi-minor axis b=sqrt(2)