What is the foci 9x^2-y^2-36x-4y+23=0 ?

The foci 9x^2-y^2-36x-4y+23=0 is (2+sqrt(10),-2),(2-sqrt(10),-2)

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foci 9x^2-y^2-36x-4y+23=0

foci

9 x^{2} - y^{2} - 36 x - 4 y + 23 = 0

(2 + 10, - 2), (2 - 10, - 2)

Solution steps

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

Calculate Hyperbola properties

9 x^{2} - y^{2} - 36 x - 4 y + 23 = 0 :

Right-left Hyperbola with

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

(2 + c, - 2), (2 - c, - 2)

Compute

c :

c = 1^{2} + 3^{2} : 10

(2 + 10, - 2), (2 - 10, - 2)

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

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

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

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

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

What is the foci 9x^2-y^2-36x-4y+23=0 ?
The foci 9x^2-y^2-36x-4y+23=0 is (2+sqrt(10),-2),(2-sqrt(10),-2)