What is the axis ((x-4)^2)/9+((y+2)^2)/(25)=1 ?

The axis ((x-4)^2)/9+((y+2)^2)/(25)=1 is semi-major axis b=5, semi-minor axis a=3

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axis ((x-4)^2)/9+((y+2)^2)/(25)=1

axis

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

semi - major axis b = 5, semi - minor axis a = 3

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

\frac{( x - 4 ) ^{2}}{3 ^{2}} + \frac{( y - ( - 2 ) ) ^{2}}{5 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (4, - 2), a = 3, b = 5

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (4, - 2), b = 5, a = 3

4 x^{2} + 24 x + 36 + 36 y^{2} - 360 y + 756 = 0

\frac{x ^{2}}{7} + \frac{y ^{2}}{16} = 1

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

4 x^{2} - 16 x + 25 y^{2} + 200 y = - 316

3 x^{(2)} + 2 y^{(2)} - 12 x + 8 y + 19 = 0

What is the axis ((x-4)^2)/9+((y+2)^2)/(25)=1 ?
The axis ((x-4)^2)/9+((y+2)^2)/(25)=1 is semi-major axis b=5, semi-minor axis a=3