What is the axis ((x-1)^2)/(13)+((y+5)^2)/(12)=1 ?

The axis ((x-1)^2)/(13)+((y+5)^2)/(12)=1 is semi-major axis a=sqrt(13), semi-minor axis b=2sqrt(3)

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axis ((x-1)^2)/(13)+((y+5)^2)/(12)=1

axis

\frac{( x - 1 ) ^{2}}{13} + \frac{( y + 5 ) ^{2}}{12} = 1

semi - major axis a = 13, semi - minor axis b = 23

Solution steps

\frac{( x - 1 ) ^{2}}{13} + \frac{( y + 5 ) ^{2}}{12} = 1

Rewrite

\frac{( x - 1 ) ^{2}}{13} + \frac{( y + 5 ) ^{2}}{12} = 1

in the form of the standard ellipse equation

\frac{( x - 1 ) ^{2}}{( 13 ) ^{2}} + \frac{( y - ( - 5 ) ) ^{2}}{( 2 3 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (1, - 5), a = 13, b = 23

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (1, - 5), a = 13, b = 23

10 x^{2} + 4 y^{2} + 2 x + 16 y = 144

\frac{( x + 8 ) ^{2}}{64} + \frac{( y - 11 ) ^{2}}{36} = 1

5 x^{2} + 20 y^{2} = 50

\frac{x ^{2}}{3} + \frac{y ^{2}}{9} = 1

16 x^{2} + 25 y^{2} + 32 x - 150 y - 159 = 0

What is the axis ((x-1)^2)/(13)+((y+5)^2)/(12)=1 ?
The axis ((x-1)^2)/(13)+((y+5)^2)/(12)=1 is semi-major axis a=sqrt(13), semi-minor axis b=2sqrt(3)