What is the foci 81x^2+972x-16y^2-128y+1364=0 ?

The foci 81x^2+972x-16y^2-128y+1364=0 is (-6+sqrt(97),-4),(-6-sqrt(97),-4)

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foci 81x^2+972x-16y^2-128y+1364=0

foci

81 x^{2} + 972 x - 16 y^{2} - 128 y + 1364 = 0

(- 6 + 97, - 4), (- 6 - 97, - 4)

Solution steps

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

Calculate Hyperbola properties

81 x^{2} + 972 x - 16 y^{2} - 128 y + 1364 = 0 :

Right-left Hyperbola with

(h, k) = (- 6, - 4), a = 4, b = 9

(- 6 + c, - 4), (- 6 - c, - 4)

Compute

c :

c = 4^{2} + 9^{2} : 97

(- 6 + 97, - 4), (- 6 - 97, - 4)

36 x^{2} - 4 y^{2} = 144

(\frac{y}{49})^{2} - (\frac{x}{36})^{2} = 1

25 y^{2} - 64 x^{2} = 1600

4 y^{2} - 16 x^{2} = 64

y^{2} - 9 x^{2} - 36 x - 8 y - 29 = 0

What is the foci 81x^2+972x-16y^2-128y+1364=0 ?
The foci 81x^2+972x-16y^2-128y+1364=0 is (-6+sqrt(97),-4),(-6-sqrt(97),-4)