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

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

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

axis

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

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

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

\frac{( x - ( - 4 ) ) ^{2}}{3 ^{2}} + \frac{( y - 9 ) ^{2}}{5 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 4, 9), a = 3, b = 5

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- 4, 9), b = 5, a = 3

x^{2} + 9 y^{2} + 6 x - 90 y + 225 = 0

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

9 x^{2} + 25 y^{2} - 36 x - 50 y + 60 = 0

25 x^{2} + 4 y^{2} = 100

36 x^{2} + 288 x + 64 y^{2} - 256 y = 1472

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