What is the foci 81x^2+4y^2=324 ?

The foci 81x^2+4y^2=324 is (0,sqrt(77)),(0,-sqrt(77))

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foci 81x^2+4y^2=324

foci

81 x^{2} + 4 y^{2} = 324

(0, 77), (0, - 77)

Solution steps

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

Calculate ellipse properties

81 x^{2} + 4 y^{2} = 324 :

Ellipse with center

(h, k) = (0, 0), b = 9, a = 2

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

Compute

c :

c = 9^{2} - 2^{2} : 77

(0, 0 + 77), (0, 0 - 77)

Refine

(0, 77), (0, - 77)

\frac{( x + 1 ) ^{2}}{64} + \frac{( y - 5 ) ^{2}}{9} = 1

\frac{( x + 2 ) ^{2}}{16} + \frac{y ^{2}}{49} = 1

16 x^{2} + 192 x + 576 + 25 y^{2} = 1600

\frac{( x - 2 ) ^{2}}{25} + \frac{( y + 1 ) ^{2}}{9} = 1

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

What is the foci 81x^2+4y^2=324 ?
The foci 81x^2+4y^2=324 is (0,sqrt(77)),(0,-sqrt(77))