What is the axis ((x-3)^2)/5+((y-1)^2)/(15)=1 ?

The axis ((x-3)^2)/5+((y-1)^2)/(15)=1 is semi-major axis b=sqrt(15), semi-minor axis a=sqrt(5)

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axis ((x-3)^2)/5+((y-1)^2)/(15)=1

axis

\frac{( x - 3 ) ^{2}}{5} + \frac{( y - 1 ) ^{2}}{15} = 1

semi - major axis b = 15, semi - minor axis a = 5

Solution steps

\frac{( x - 3 ) ^{2}}{5} + \frac{( y - 1 ) ^{2}}{15} = 1

Rewrite

\frac{( x - 3 ) ^{2}}{5} + \frac{( y - 1 ) ^{2}}{15} = 1

in the form of the standard ellipse equation

\frac{( x - 3 ) ^{2}}{( 5 ) ^{2}} + \frac{( y - 1 ) ^{2}}{( 15 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (3, 1), a = 5, b = 15

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (3, 1), b = 15, a = 5

9 X^{2} + 4 Y^{2} = 36

25 x^{2} - 200 x + y^{2} + 4 y + 379 = 0

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

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

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

What is the axis ((x-3)^2)/5+((y-1)^2)/(15)=1 ?
The axis ((x-3)^2)/5+((y-1)^2)/(15)=1 is semi-major axis b=sqrt(15), semi-minor axis a=sqrt(5)