What is the foci-9x^2+y^2+18x-45=0 ?

The foci-9x^2+y^2+18x-45=0 is (1,2sqrt(10)),(1,-2sqrt(10))

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foci-9x^2+y^2+18x-45=0

foci

- 9 x^{2} + y^{2} + 18 x - 45 = 0

(1, 210), (1, - 210)

Solution steps

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

Calculate Hyperbola properties

- 9 x^{2} + y^{2} + 18 x - 45 = 0 :

Up-down Hyperbola with

(h, k) = (1, 0), a = 6, b = 2

(1, 0 + c), (1, 0 - c)

Compute

c :

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

(1, 0 + 210), (1, 0 - 210)

Refine

(1, 210), (1, - 210)

\frac{( y - 4 ) ^{2}}{25} - \frac{( x + 1 ) ^{2}}{4} = 1

+ \frac{x ^{2}}{49} - \frac{y ^{2}}{9} = 1

9 x^{2} - 4 y^{2} + 54 x - 8 y + 78 = 0

9 x^{2} - 36 x - 4 y^{2} - 24 y - 36 = 0

\frac{( x - 3 ) ^{2}}{81} - \frac{( y + 5 ) ^{2}}{144} = 1

What is the foci-9x^2+y^2+18x-45=0 ?
The foci-9x^2+y^2+18x-45=0 is (1,2sqrt(10)),(1,-2sqrt(10))