What is the axis ((x-5)^2)/(49)+((y-9)^2)/(25)=1 ?

The axis ((x-5)^2)/(49)+((y-9)^2)/(25)=1 is semi-major axis a=7, semi-minor axis b=5

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axis ((x-5)^2)/(49)+((y-9)^2)/(25)=1

axis

\frac{( x - 5 ) ^{2}}{49} + \frac{( y - 9 ) ^{2}}{25} = 1

semi - major axis a = 7, semi - minor axis b = 5

Solution steps

\frac{( x - 5 ) ^{2}}{49} + \frac{( y - 9 ) ^{2}}{25} = 1

Rewrite

\frac{( x - 5 ) ^{2}}{49} + \frac{( y - 9 ) ^{2}}{25} = 1

in the form of the standard ellipse equation

\frac{( x - 5 ) ^{2}}{7 ^{2}} + \frac{( y - 9 ) ^{2}}{5 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (5, 9), a = 7, b = 5

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (5, 9), a = 7, b = 5

\frac{x ^{2}}{56} + \frac{y ^{2}}{36} = 1

25 x^{2} + 16 y^{2} + 100 x + 96 y - 156 = 0

\frac{( x - 5 ) ^{2}}{9} + \frac{( y - 3 ) ^{2}}{16} = 1

3 x^{2} + 7 y^{2} = 63

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

What is the axis ((x-5)^2)/(49)+((y-9)^2)/(25)=1 ?
The axis ((x-5)^2)/(49)+((y-9)^2)/(25)=1 is semi-major axis a=7, semi-minor axis b=5