What is the axis 9x^2+9y^2+18x-18y+14=0 ?

The axis 9x^2+9y^2+18x-18y+14=0 is semi-major axis b= 2/3 , semi-minor axis a= 2/3

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axis 9x^2+9y^2+18x-18y+14=0

axis

9 x^{2} + 9 y^{2} + 18 x - 18 y + 14 = 0

semi - major axis b = \frac{2}{3}, semi - minor axis a = \frac{2}{3}

Solution steps

9 x^{2} + 9 y^{2} + 18 x - 18 y + 14 = 0

Rewrite

9 x^{2} + 9 y^{2} + 18 x - 18 y + 14 = 0

in the form of the standard ellipse equation

\frac{( x - ( - 1 ) ) ^{2}}{( \frac{2}{3} ) ^{2}} + \frac{( y - 1 ) ^{2}}{( \frac{2}{3} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 1, 1), a = \frac{2}{3}, b = \frac{2}{3}

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- 1, 1), b = \frac{2}{3}, a = \frac{2}{3}

\frac{x ^{2}}{49} + \frac{y ^{2}}{9} = 1

\frac{x ^{2}}{8} + \frac{y ^{2}}{3} = 1

\frac{x ^{2}}{36} + \frac{y ^{2}}{4} = 1

\frac{x ^{2}}{63500} + \frac{y ^{2}}{50900} = 1

25 x^{2} + 9 y^{2} = 225

What is the axis 9x^2+9y^2+18x-18y+14=0 ?
The axis 9x^2+9y^2+18x-18y+14=0 is semi-major axis b= 2/3 , semi-minor axis a= 2/3