What is the foci 9x^2-18x-24y-63=4y^2 ?

The foci 9x^2-18x-24y-63=4y^2 is (1+sqrt(13),-3),(1-sqrt(13),-3)

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foci 9x^2-18x-24y-63=4y^2

foci

9 x^{2} - 18 x - 24 y - 63 = 4 y^{2}

(1 + 13, - 3), (1 - 13, - 3)

Solution steps

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

Calculate Hyperbola properties

9 x^{2} - 18 x - 24 y - 63 = 4 y^{2} :

Right-left Hyperbola with

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

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

Compute

c :

c = 2^{2} + 3^{2} : 13

(1 + 13, - 3), (1 - 13, - 3)

36 x^{2} - 25 y^{2} = 900

\frac{x ^{2}}{36} - \frac{y ^{2}}{4} = 1

- 9 x^{2} - 32 y = - 16 y^{2} + 128

\frac{x ^{2}}{16} - \frac{y ^{2}}{16} = 1

16 y^{2} - x^{2} + 2 x + 64 y + 47 = 0

What is the foci 9x^2-18x-24y-63=4y^2 ?
The foci 9x^2-18x-24y-63=4y^2 is (1+sqrt(13),-3),(1-sqrt(13),-3)