What is the foci ((x+7)^2)/(90)+((y+8)^2)/(84)=1 ?

The foci ((x+7)^2)/(90)+((y+8)^2)/(84)=1 is (-7+sqrt(6),-8),(-7-sqrt(6),-8)

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foci ((x+7)^2)/(90)+((y+8)^2)/(84)=1

foci

\frac{( x + 7 ) ^{2}}{90} + \frac{( y + 8 ) ^{2}}{84} = 1

(- 7 + 6, - 8), (- 7 - 6, - 8)

Solution steps

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

Calculate ellipse properties

\frac{( x + 7 ) ^{2}}{90} + \frac{( y + 8 ) ^{2}}{84} = 1 :

Ellipse with center

(h, k) = (- 7, - 8), a = 310, b = 221

(- 7 + c, - 8), (- 7 - c, - 8)

Compute

c :

c = (310)^{2} - (221)^{2} : 6

(- 7 + 6, - 8), (- 7 - 6, - 8)

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

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

x^{2} + 4 x + 2 y^{2} + 6 y + 1 = 0

25 x^{2} + 81 y^{2} = 2025

x^{2} + 9 y^{2} - 14 x + 36 y + 49 = 0

What is the foci ((x+7)^2)/(90)+((y+8)^2)/(84)=1 ?
The foci ((x+7)^2)/(90)+((y+8)^2)/(84)=1 is (-7+sqrt(6),-8),(-7-sqrt(6),-8)