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

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

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axis ((x-1)^2)/(a^2)+((y-3)^2)/(b^2)=1

axis

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

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

Solution steps

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

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

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

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

\frac{x ^{2}}{4} + \frac{y ^{2}}{9} = 4

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

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