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

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

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

foci

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

(- 2, 1 + 17), (- 2, 1 - 17)

Solution steps

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

Calculate ellipse properties

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

Ellipse with center

(h, k) = (- 2, 1), b = 9, a = 8

(- 2, 1 + c), (- 2, 1 - c)

Compute

c :

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

(- 2, 1 + 17), (- 2, 1 - 17)

4 x^{2} + 25 y^{2} - 100 = 0

25 x^{2} + 9 y^{2} - 225 = 0

\frac{( x - 1 ) ^{2}}{36} + \frac{( y - 1 ) ^{2}}{25} = 1

9 x^{2} + 16 y^{2} + 72 x + 128 y + 256 = 0

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

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