What is the foci ((x-3)^2)/(64)+((y+5)^2)/(81)=1 ?

The foci ((x-3)^2)/(64)+((y+5)^2)/(81)=1 is (3,-5+sqrt(17)),(3,-5-sqrt(17))

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foci ((x-3)^2)/(64)+((y+5)^2)/(81)=1

foci

\frac{( x - 3 ) ^{2}}{64} + \frac{( y + 5 ) ^{2}}{81} = 1

(3, - 5 + 17), (3, - 5 - 17)

Solution steps

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

Calculate ellipse properties

\frac{( x - 3 ) ^{2}}{64} + \frac{( y + 5 ) ^{2}}{81} = 1 :

Ellipse with center

(h, k) = (3, - 5), b = 9, a = 8

(3, - 5 + c), (3, - 5 - c)

Compute

c :

c = 9^{2} - 8^{2} : 17

(3, - 5 + 17), (3, - 5 - 17)

5 x^{2} + 9 y^{2} - 10 x - 36 y = 4

\frac{x ^{2}}{36} + \frac{y ^{2}}{27} = 1

x^{2} + \frac{y ^{2}}{5} = 1

x^{2} + 4 y^{2} + 4 x = 0

\frac{( x - 1 ) ^{2}}{6} + \frac{( y + 2 ) ^{2}}{18} = 1

What is the foci ((x-3)^2)/(64)+((y+5)^2)/(81)=1 ?
The foci ((x-3)^2)/(64)+((y+5)^2)/(81)=1 is (3,-5+sqrt(17)),(3,-5-sqrt(17))