What is the foci ((x)^2)/(46)+((y+8)^2)/(26)=1 ?

The foci ((x)^2)/(46)+((y+8)^2)/(26)=1 is (2sqrt(5),-8),(-2sqrt(5),-8)

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foci ((x)^2)/(46)+((y+8)^2)/(26)=1

foci

\frac{( x ) ^{2}}{46} + \frac{( y + 8 ) ^{2}}{26} = 1

(25, - 8), (- 25, - 8)

Solution steps

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

Calculate ellipse properties

\frac{x ^{2}}{46} + \frac{( y + 8 ) ^{2}}{26} = 1 :

Ellipse with center

(h, k) = (0, - 8), a = 46, b = 26

(0 + c, - 8), (0 - c, - 8)

Compute

c :

c = 46^{2} - 26^{2} : 25

(0 + 25, - 8), (0 - 25, - 8)

Refine

(25, - 8), (- 25, - 8)

\frac{( x - 4 ) ^{2}}{4} + \frac{( y - 5 ) ^{2}}{25} = 1

81 x^{2} + 36 y^{2} = 2916

5 x^{2} + 7 y^{2} = 70

x^{2} + 9 y^{2} + 4 x = 5

4 x^{2} - 40 x + 2 y^{2} - 20 y = - 142

What is the foci ((x)^2)/(46)+((y+8)^2)/(26)=1 ?
The foci ((x)^2)/(46)+((y+8)^2)/(26)=1 is (2sqrt(5),-8),(-2sqrt(5),-8)