What is the foci-x^2+4y^2-8y-12=0 ?

The foci-x^2+4y^2-8y-12=0 is (0,1+2sqrt(5)),(0,1-2sqrt(5))

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foci-x^2+4y^2-8y-12=0

foci

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

(0, 1 + 25), (0, 1 - 25)

Solution steps

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

Calculate Hyperbola properties

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

Up-down Hyperbola with

(h, k) = (0, 1), a = 2, b = 4

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

Compute

c :

c = 2^{2} + 4^{2} : 25

(0, 1 + 25), (0, 1 - 25)

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

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

What is the foci-x^2+4y^2-8y-12=0 ?
The foci-x^2+4y^2-8y-12=0 is (0,1+2sqrt(5)),(0,1-2sqrt(5))