What is the axis x^2+2y^2+2x-4y-1=0 ?

The axis x^2+2y^2+2x-4y-1=0 is semi-major axis a=2, semi-minor axis b=sqrt(2)

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axis x^2+2y^2+2x-4y-1=0

axis

x^{2} + 2 y^{2} + 2 x - 4 y - 1 = 0

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

Solution steps

x^{2} + 2 y^{2} + 2 x - 4 y - 1 = 0

Rewrite

x^{2} + 2 y^{2} + 2 x - 4 y - 1 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

27 x^{2} + 48 y^{2} - 54 x - 192 y - 213 = 0

4 x^{2} + 25 y^{2} + 32 x - 250 y + 589 = 0

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

\frac{x ^{2}}{36} + \frac{y ^{2}}{100} = 1

9 x^{2} + 25 y^{2} = 900

What is the axis x^2+2y^2+2x-4y-1=0 ?
The axis x^2+2y^2+2x-4y-1=0 is semi-major axis a=2, semi-minor axis b=sqrt(2)