What is the foci 4x^2-9y^2-8x+72y-176=0 ?

The foci 4x^2-9y^2-8x+72y-176=0 is (1+sqrt(13),4),(1-sqrt(13),4)

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foci 4x^2-9y^2-8x+72y-176=0

foci

4 x^{2} - 9 y^{2} - 8 x + 72 y - 176 = 0

(1 + 13, 4), (1 - 13, 4)

Solution steps

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

Calculate Hyperbola properties

4 x^{2} - 9 y^{2} - 8 x + 72 y - 176 = 0 :

Right-left Hyperbola with

(h, k) = (1, 4), a = 3, b = 2

(1 + c, 4), (1 - c, 4)

Compute

c :

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

(1 + 13, 4), (1 - 13, 4)

- x^{2} + 4 y^{2} - 8 y - 12 = 0

3 y^{2} - 12 x^{2} - 36 y - 48 x + 48 = 0

\frac{y ^{2}}{16} - \frac{x ^{2}}{20} = 1

\frac{( y + 5 ) ^{2}}{64} - \frac{( x + 2 ) ^{2}}{36} = 1

\frac{x ^{2}}{1} - \frac{y ^{2}}{35} = 1

What is the foci 4x^2-9y^2-8x+72y-176=0 ?
The foci 4x^2-9y^2-8x+72y-176=0 is (1+sqrt(13),4),(1-sqrt(13),4)