What is the foci 9x^2-4y^2+72x+180=0 ?

The foci 9x^2-4y^2+72x+180=0 is (-4,sqrt(13)),(-4,-sqrt(13))

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foci 9x^2-4y^2+72x+180=0

foci

9 x^{2} - 4 y^{2} + 72 x + 180 = 0

(- 4, 13), (- 4, - 13)

Solution steps

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

Calculate Hyperbola properties

9 x^{2} - 4 y^{2} + 72 x + 180 = 0 :

Up-down Hyperbola with

(h, k) = (- 4, 0), a = 3, b = 2

(- 4, 0 + c), (- 4, 0 - c)

Compute

c :

c = 3^{2} + 2^{2} : 13

(- 4, 0 + 13), (- 4, 0 - 13)

Refine

(- 4, 13), (- 4, - 13)

1 = x^{2} - y^{2}

\frac{x ^{2}}{900} - \frac{y ^{2}}{1600} = 1

y^{2} - 9 x^{2} = 9

10 y^{2} - 5 x^{2} = 50

\frac{( x - 1 ) ^{2}}{9} - \frac{( y - 3 ) ^{2}}{16} = 1

What is the foci 9x^2-4y^2+72x+180=0 ?
The foci 9x^2-4y^2+72x+180=0 is (-4,sqrt(13)),(-4,-sqrt(13))