What is the foci 3y^2-12x^2-36y-48x+48=0 ?

The foci 3y^2-12x^2-36y-48x+48=0 is (-2,6+sqrt(5)),(-2,6-sqrt(5))

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

foci

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

(- 2, 6 + 5), (- 2, 6 - 5)

Solution steps

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

Calculate Hyperbola properties

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

Up-down Hyperbola with

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

(- 2, 6 + c), (- 2, 6 - c)

Compute

c :

c = 2^{2} + 1^{2} : 5

(- 2, 6 + 5), (- 2, 6 - 5)

\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

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

9 x^{2} - 9 y^{2} + 18 x + 36 y = 63

What is the foci 3y^2-12x^2-36y-48x+48=0 ?
The foci 3y^2-12x^2-36y-48x+48=0 is (-2,6+sqrt(5)),(-2,6-sqrt(5))