What is the axis ((x-2)^2)/(36)+((y+1)^2)/(25)=1 ?

The axis ((x-2)^2)/(36)+((y+1)^2)/(25)=1 is semi-major axis a=6, semi-minor axis b=5

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axis ((x-2)^2)/(36)+((y+1)^2)/(25)=1

axis

\frac{( x - 2 ) ^{2}}{36} + \frac{( y + 1 ) ^{2}}{25} = 1

semi - major axis a = 6, semi - minor axis b = 5

Solution steps

\frac{( x - 2 ) ^{2}}{36} + \frac{( y + 1 ) ^{2}}{25} = 1

Rewrite

\frac{( x - 2 ) ^{2}}{36} + \frac{( y + 1 ) ^{2}}{25} = 1

in the form of the standard ellipse equation

\frac{( x - 2 ) ^{2}}{6 ^{2}} + \frac{( y - ( - 1 ) ) ^{2}}{5 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (2, - 1), a = 6, b = 5

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (2, - 1), a = 6, b = 5

\frac{x ^{2}}{81} + \frac{y ^{2}}{16} = 1

\frac{( x - 2 ) ^{2}}{64} + \frac{( y + 4 ) ^{2}}{16} = 1

9 x^{2} + 16 y^{2} - 54 x + 64 y + 1 = 0

\frac{( x - 1 ) ^{2}}{9} + \frac{( y + 5 ) ^{2}}{16} = 1

\frac{( y + 4 ) ^{2}}{9} + \frac{( x - 9 ) ^{2}}{25} = 1

What is the axis ((x-2)^2)/(36)+((y+1)^2)/(25)=1 ?
The axis ((x-2)^2)/(36)+((y+1)^2)/(25)=1 is semi-major axis a=6, semi-minor axis b=5