What is the axis x^2+2y^2+2x-8y+7=0 ?

The axis x^2+2y^2+2x-8y+7=0 is semi-major axis a=sqrt(2), semi-minor axis b=1

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axis x^2+2y^2+2x-8y+7=0

axis

x^{2} + 2 y^{2} + 2 x - 8 y + 7 = 0

semi - major axis a = 2, semi - minor axis b = 1

Solution steps

x^{2} + 2 y^{2} + 2 x - 8 y + 7 = 0

Rewrite

x^{2} + 2 y^{2} + 2 x - 8 y + 7 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

\frac{x ^{2}}{36} + \frac{y ^{2}}{11} = 1

36 x^{2} + 11 y^{2} + 144 x + 44 y - 208 = 0

9 x^{2} + 16 y^{2} + 90 x + 32 y + 97 = 0

\frac{( x - 4 ) ^{2}}{4} + \frac{y ^{2}}{16} = 1

x^{2} + 4 y^{2} - 6 x + 12 y - 11 = 0

What is the axis x^2+2y^2+2x-8y+7=0 ?
The axis x^2+2y^2+2x-8y+7=0 is semi-major axis a=sqrt(2), semi-minor axis b=1