What is the foci y^2-49x^2-14y-490x-1125=0 ?

The foci y^2-49x^2-14y-490x-1125=0 is ((-35+5sqrt(102))/7 ,7),((-35-5sqrt(102))/7 ,7)

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foci y^2-49x^2-14y-490x-1125=0

foci

y^{2} - 49 x^{2} - 14 y - 490 x - 1125 = 0

(\frac{- 35 + 5 102}{7}, 7), (\frac{- 35 - 5 102}{7}, 7)

Solution steps

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

Calculate Hyperbola properties

y^{2} - 49 x^{2} - 14 y - 490 x - 1125 = 0 :

Right-left Hyperbola with

(h, k) = (- 5, 7), a = \frac{51}{7}, b = 51

(- 5 + c, 7), (- 5 - c, 7)

Compute

c :

c = (\frac{51}{7})^{2} + 51^{2} : \frac{5 102}{7}

(- 5 + \frac{5 102}{7}, 7), (- 5 - \frac{5 102}{7}, 7)

Refine

(\frac{- 35 + 5 102}{7}, 7), (\frac{- 35 - 5 102}{7}, 7)

\frac{x ^{2}}{25} - \frac{y ^{2}}{4} = 1

4 y^{2} - x^{2} + 6 x + 8 y + 4 = 0

- 9 x^{2} + y^{2} + 6 y - 27 = 0

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

\frac{( y + 1 ) ^{2}}{49} - \frac{( x + 3 ) ^{2}}{64} = 1

What is the foci y^2-49x^2-14y-490x-1125=0 ?
The foci y^2-49x^2-14y-490x-1125=0 is ((-35+5sqrt(102))/7 ,7),((-35-5sqrt(102))/7 ,7)