What is the foci ((x+20)^2)/(16)+(y^2)/(89)=1 ?

The foci ((x+20)^2)/(16)+(y^2)/(89)=1 is (-20,sqrt(73)),(-20,-sqrt(73))

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foci ((x+20)^2)/(16)+(y^2)/(89)=1

foci

\frac{( x + 20 ) ^{2}}{16} + \frac{y ^{2}}{89} = 1

(- 20, 73), (- 20, - 73)

Solution steps

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

Calculate ellipse properties

\frac{( x + 20 ) ^{2}}{16} + \frac{y ^{2}}{89} = 1 :

Ellipse with center

(h, k) = (- 20, 0), b = 89, a = 4

(- 20, 0 + c), (- 20, 0 - c)

Compute

c :

c = 89^{2} - 4^{2} : 73

(- 20, 0 + 73), (- 20, 0 - 73)

Refine

(- 20, 73), (- 20, - 73)

\frac{x ^{2}}{\frac{9}{4}} + \frac{y ^{2}}{\frac{25}{4}} = 1

\frac{( x - 3 ) ^{2}}{25} + \frac{( y - 3 ) ^{2}}{4} = 1

\frac{( x - 3 ) ^{2}}{25} + \frac{( y + 3 ) ^{2}}{4} = 1

\frac{( x - 8 ) ^{2}}{2} + \frac{( y - 3 ) ^{2}}{27} = 1

x^{2} + 4 y^{2} + 6 x + 16 y + 21 = 0

What is the foci ((x+20)^2)/(16)+(y^2)/(89)=1 ?
The foci ((x+20)^2)/(16)+(y^2)/(89)=1 is (-20,sqrt(73)),(-20,-sqrt(73))