What is the axis ((x+6)^2}{18}+\frac{(y+3)^2)/9 =1 ?

The axis ((x+6)^2}{18}+\frac{(y+3)^2)/9 =1 is semi-major axis a=3sqrt(2), semi-minor axis b=3

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axis ((x+6)^2}{18}+\frac{(y+3)^2)/9 =1

axis

\frac{( x + 6 ) ^{2}}{18} + \frac{( y + 3 ) ^{2}}{9} = 1

semi - major axis a = 32, semi - minor axis b = 3

Solution steps

\frac{( x + 6 ) ^{2}}{18} + \frac{( y + 3 ) ^{2}}{9} = 1

Rewrite

\frac{( x + 6 ) ^{2}}{18} + \frac{( y + 3 ) ^{2}}{9} = 1

in the form of the standard ellipse equation

\frac{( x - ( - 6 ) ) ^{2}}{( 3 2 ) ^{2}} + \frac{( y - ( - 3 ) ) ^{2}}{3 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 6, - 3), a = 32, b = 3

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 6, - 3), a = 32, b = 3

\frac{x ^{2}}{16} + y^{2} = 1

3 x^{2} + 7 y^{2} - 12 x - 28 y + 19 = 0

x^{2} + y^{2} - 6 y = 0

\frac{x ^{2}}{20} + \frac{y ^{2}}{4} = 1

25 x^{2} + 4 y^{2} + 50 x - 16 y - 59 = 0

What is the axis ((x+6)^2}{18}+\frac{(y+3)^2)/9 =1 ?
The axis ((x+6)^2}{18}+\frac{(y+3)^2)/9 =1 is semi-major axis a=3sqrt(2), semi-minor axis b=3