What is the foci 81x^2+49y^2=3969 ?

The foci 81x^2+49y^2=3969 is (0,4sqrt(2)),(0,-4sqrt(2))

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foci 81x^2+49y^2=3969

foci

81 x^{2} + 49 y^{2} = 3969

(0, 42), (0, - 42)

Solution steps

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

Calculate ellipse properties

81 x^{2} + 49 y^{2} = 3969 :

Ellipse with center

(h, k) = (0, 0), b = 9, a = 7

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

Compute

c :

c = 9^{2} - 7^{2} : 42

(0, 0 + 42), (0, 0 - 42)

Refine

(0, 42), (0, - 42)

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

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

\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

What is the foci 81x^2+49y^2=3969 ?
The foci 81x^2+49y^2=3969 is (0,4sqrt(2)),(0,-4sqrt(2))