What is the foci y^2-4x^2-10y-40x-100=0 ?

The foci y^2-4x^2-10y-40x-100=0 is (-5,(10+5sqrt(5))/2),(-5,(10-5sqrt(5))/2)

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foci y^2-4x^2-10y-40x-100=0

foci

y^{2} - 4 x^{2} - 10 y - 40 x - 100 = 0

(- 5, \frac{10 + 5 5}{2}), (- 5, \frac{10 - 5 5}{2})

Solution steps

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

Calculate Hyperbola properties

y^{2} - 4 x^{2} - 10 y - 40 x - 100 = 0 :

Up-down Hyperbola with

(h, k) = (- 5, 5), a = 5, b = \frac{5}{2}

(- 5, 5 + c), (- 5, 5 - c)

Compute

c :

c = 5^{2} + (\frac{5}{2})^{2} : \frac{5 5}{2}

(- 5, 5 + \frac{5 5}{2}), (- 5, 5 - \frac{5 5}{2})

Refine

(- 5, \frac{10 + 5 5}{2}), (- 5, \frac{10 - 5 5}{2})

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

\frac{( x ^{2} )}{4} - 0.15 y^{2} = 1

9 x^{2} - y^{2} - 36 x - 6 y + 18 = 0

\frac{x ^{2}}{4} - \frac{( y + 1 ) ^{2}}{16} = 1

\frac{( x - 5 ) ^{2}}{4} - \frac{( y + 5 ) ^{2}}{9} = 1

What is the foci y^2-4x^2-10y-40x-100=0 ?
The foci y^2-4x^2-10y-40x-100=0 is (-5,(10+5sqrt(5))/2),(-5,(10-5sqrt(5))/2)