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

The foci ((x-1)^2)/9+(y^2)/4 =1 is (1+sqrt(5),0),(1-sqrt(5),0)

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

foci

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

(1 + 5, 0), (1 - 5, 0)

Solution steps

(h + c, k), (h - c, k)

Calculate ellipse properties

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

Ellipse with center

(h, k) = (1, 0), a = 3, b = 2

(1 + c, 0), (1 - c, 0)

Compute

c :

c = 3^{2} - 2^{2} : 5

(1 + 5, 0), (1 - 5, 0)

4 x^{2} + 9 y^{2} + 16 x - 90 y + 205 = 0

9 x^{2} + 4 y^{2} - 18 x - 16 y - 11 = 0

\frac{( x - 1 ) ^{2}}{36} + \frac{( y - 2 ) ^{2}}{115} = 3

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

\frac{( x - 3 ) ^{2}}{100} + \frac{( y - 1 ) ^{2}}{64} = 1

What is the foci ((x-1)^2)/9+(y^2)/4 =1 ?
The foci ((x-1)^2)/9+(y^2)/4 =1 is (1+sqrt(5),0),(1-sqrt(5),0)