What is the foci 4x^2-24x-25y^2+250y-489=0 ?

The foci 4x^2-24x-25y^2+250y-489=0 is (3,5+sqrt(29)),(3,5-sqrt(29))

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foci 4x^2-24x-25y^2+250y-489=0

foci

4 x^{2} - 24 x - 25 y^{2} + 250 y - 489 = 0

(3, 5 + 29), (3, 5 - 29)

Solution steps

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

Calculate Hyperbola properties

4 x^{2} - 24 x - 25 y^{2} + 250 y - 489 = 0 :

Up-down Hyperbola with

(h, k) = (3, 5), a = 2, b = 5

(3, 5 + c), (3, 5 - c)

Compute

c :

c = 2^{2} + 5^{2} : 29

(3, 5 + 29), (3, 5 - 29)

\frac{x ^{2}}{9} - y^{2} = 1

9 y^{2} - 4 x^{2} + 32 x - 36 y - 64 = 0

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

x^{2} + 6 x = 9 y^{2}

\frac{x ^{2}}{140} - \frac{( y - 6 ) ^{2}}{4} = 1

What is the foci 4x^2-24x-25y^2+250y-489=0 ?
The foci 4x^2-24x-25y^2+250y-489=0 is (3,5+sqrt(29)),(3,5-sqrt(29))