What is the axis ((x-1)^2)/6+((y-3)^2)/2 =1 ?

The axis ((x-1)^2)/6+((y-3)^2)/2 =1 is semi-major axis a=sqrt(6), semi-minor axis b=sqrt(2)

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axis ((x-1)^2)/6+((y-3)^2)/2 =1

axis

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

semi - major axis a = 6, semi - minor axis b = 2

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (1, 3), a = 6, b = 2

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (1, 3), a = 6, b = 2

\frac{x ^{2}}{64} + \frac{y ^{2}}{100} = 1

\frac{x ^{2}}{9} + \frac{y ^{2}}{16} > 1

\frac{x ^{2}}{16} + \frac{y ^{2}}{12} = 1

9 x^{2} + 25 y^{2} + 18 x + 150 y + 9 = 0

25 x^{2} + 144 y^{2} = 900

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