What is the foci (x^2)/(9^2)+(y^2)/(6^2)=1 ?

The foci (x^2)/(9^2)+(y^2)/(6^2)=1 is (3sqrt(5),0),(-3sqrt(5),0)

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foci (x^2)/(9^2)+(y^2)/(6^2)=1

foci

\frac{x ^{2}}{9 ^{2}} + \frac{y ^{2}}{6 ^{2}} = 1

(35, 0), (- 35, 0)

Solution steps

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

Calculate ellipse properties

\frac{x ^{2}}{9 ^{2}} + \frac{y ^{2}}{6 ^{2}} = 1 :

Ellipse with center

(h, k) = (0, 0), a = 9, b = 6

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

Compute

c :

c = 9^{2} - 6^{2} : 35

(0 + 35, 0), (0 - 35, 0)

Refine

(35, 0), (- 35, 0)

\frac{x ^{2}}{5 ^{2}} + \frac{y ^{2}}{1 3 ^{2}} = 1

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

\frac{( y + 3 ) ^{2}}{169} + \frac{( x + 2 ) ^{2}}{25} = 1

\frac{x ^{2}}{15} + \frac{y ^{2}}{45} = 1

9 x^{2} + 16 y^{2} + 96 y = 0

What is the foci (x^2)/(9^2)+(y^2)/(6^2)=1 ?
The foci (x^2)/(9^2)+(y^2)/(6^2)=1 is (3sqrt(5),0),(-3sqrt(5),0)