What is the foci 9y^2-x^2+2x+54y+62=0 ?

The foci 9y^2-x^2+2x+54y+62=0 is (1,-3+2sqrt(5)),(1,-3-2sqrt(5))

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foci 9y^2-x^2+2x+54y+62=0

foci

9 y^{2} - x^{2} + 2 x + 54 y + 62 = 0

(1, - 3 + 25), (1, - 3 - 25)

Solution steps

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

Calculate Hyperbola properties

9 y^{2} - x^{2} + 2 x + 54 y + 62 = 0 :

Up-down Hyperbola with

(h, k) = (1, - 3), a = 2, b = 32

(1, - 3 + c), (1, - 3 - c)

Compute

c :

c = 2^{2} + (32)^{2} : 25

(1, - 3 + 25), (1, - 3 - 25)

16 x^{2} - 25 y^{2} = 400

9 y^{2} - 16 x^{2} = 144

\frac{x ^{2}}{144} - \frac{y ^{2}}{25} = 1

\frac{y ^{2}}{25} - \frac{x ^{2}}{81} = 1

\frac{( x - 5 ) ^{2}}{16} - \frac{( y + 7 ) ^{2}}{9} = - 1

What is the foci 9y^2-x^2+2x+54y+62=0 ?
The foci 9y^2-x^2+2x+54y+62=0 is (1,-3+2sqrt(5)),(1,-3-2sqrt(5))