What is the foci-9x^2+y^2+54x-117=0 ?

The foci-9x^2+y^2+54x-117=0 is (3,2sqrt(10)),(3,-2sqrt(10))

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foci-9x^2+y^2+54x-117=0

foci

- 9 x^{2} + y^{2} + 54 x - 117 = 0

(3, 210), (3, - 210)

Solution steps

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

Calculate Hyperbola properties

- 9 x^{2} + y^{2} + 54 x - 117 = 0 :

Up-down Hyperbola with

(h, k) = (3, 0), a = 6, b = 2

(3, 0 + c), (3, 0 - c)

Compute

c :

c = 6^{2} + 2^{2} : 210

(3, 0 + 210), (3, 0 - 210)

Refine

(3, 210), (3, - 210)

\frac{( y ^{2} )}{27} - \frac{( x ^{2} )}{9} = 1

64 x^{2} - 100 y^{2} = 6400

(\frac{( x ^{2} )}{27}) - \frac{( ( y - 3 ) ^{2} )}{36} = 1

\frac{( x - 7 ) ^{2}}{25} - \frac{y ^{2}}{16} = 1

\frac{x ^{2}}{5} - \frac{y ^{2}}{7} = 1

What is the foci-9x^2+y^2+54x-117=0 ?
The foci-9x^2+y^2+54x-117=0 is (3,2sqrt(10)),(3,-2sqrt(10))