What is the foci (x^2)/(36)+(8y^2)/(81)=1 ?

The foci (x^2)/(36)+(8y^2)/(81)=1 is ((3sqrt(23))/(2sqrt(2)),0),(-(3sqrt(23))/(2sqrt(2)),0)

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foci (x^2)/(36)+(8y^2)/(81)=1

foci

\frac{x ^{2}}{36} + \frac{8 y ^{2}}{81} = 1

(\frac{3 23}{2 2}, 0), (- \frac{3 23}{2 2}, 0)

Solution steps

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

Calculate ellipse properties

\frac{x ^{2}}{36} + \frac{8 y ^{2}}{81} = 1 :

Ellipse with center

(h, k) = (0, 0), a = 6, b = \frac{9}{2 2}

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

Compute

c :

c = 6^{2} - (\frac{9}{2 2})^{2} : \frac{3 23}{2 2}

(0 + \frac{3 23}{2 2}, 0), (0 - \frac{3 23}{2 2}, 0)

Refine

(\frac{3 23}{2 2}, 0), (- \frac{3 23}{2 2}, 0)

x^{2} + 3 y^{2} + 8 x + 9 y - 14 = 0

\frac{x ^{2}}{4} + \frac{y ^{2}}{13} = 1

\frac{( x - 3 ) ^{2}}{9} + \frac{( y + 2 ) ^{2}}{25} = 1

25 \frac{x ^{2}}{4} - 50 x + 100 y^{2} + 800 y + 1075 = 0

x^{2} + 16 y^{2} = 1

What is the foci (x^2)/(36)+(8y^2)/(81)=1 ?
The foci (x^2)/(36)+(8y^2)/(81)=1 is ((3sqrt(23))/(2sqrt(2)),0),(-(3sqrt(23))/(2sqrt(2)),0)