What is the foci 5x^2-5y^2+20x-60y=185 ?

The foci 5x^2-5y^2+20x-60y=185 is (-2+sqrt(10),-6),(-2-sqrt(10),-6)

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foci 5x^2-5y^2+20x-60y=185

foci

5 x^{2} - 5 y^{2} + 20 x - 60 y = 185

(- 2 + 10, - 6), (- 2 - 10, - 6)

Solution steps

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

Calculate Hyperbola properties

5 x^{2} - 5 y^{2} + 20 x - 60 y = 185 :

Right-left Hyperbola with

(h, k) = (- 2, - 6), a = 5, b = 5

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

Compute

c :

c = 5^{2} + 5^{2} : 10

(- 2 + 10, - 6), (- 2 - 10, - 6)

\frac{x ^{2}}{25} - \frac{y ^{2}}{36} = 1

25 y^{2} - 16 x^{2} = 400

\frac{x ^{2}}{9} - \frac{y ^{2}}{49} = 1

4 x^{2} - 3 y^{2} - 8 x - 8 = 0

\frac{( x - 3 ) ^{2}}{25} - \frac{( y + 1 ) ^{2}}{25} = 1

What is the foci 5x^2-5y^2+20x-60y=185 ?
The foci 5x^2-5y^2+20x-60y=185 is (-2+sqrt(10),-6),(-2-sqrt(10),-6)