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

The foci ((x-1)^2)/9+((y-5)^2)/(25)=1 is (1,9),(1,1)

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

foci

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

(1, 9), (1, 1)

Solution steps

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

Calculate ellipse properties

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

Ellipse with center

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

(1, 5 + c), (1, 5 - c)

Compute

c :

c = 5^{2} - 3^{2} : 4

(1, 5 + 4), (1, 5 - 4)

Refine

(1, 9), (1, 1)

16 x^{2} + 64 x + 4 y^{2} - 8 y + 4 = 0

\frac{x ^{2}}{17} + \frac{y ^{2}}{35} = 1

64 x^{2} + 81 y^{2} = 5184

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

4 x^{2} + y^{2} + 40 x + 6 y + 95 = 0

What is the foci ((x-1)^2)/9+((y-5)^2)/(25)=1 ?
The foci ((x-1)^2)/9+((y-5)^2)/(25)=1 is (1,9),(1,1)