What is the foci 4x^2-y^2-32x+60=0 ?

The foci 4x^2-y^2-32x+60=0 is (4+sqrt(5),0),(4-sqrt(5),0)

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foci 4x^2-y^2-32x+60=0

foci

4 x^{2} - y^{2} - 32 x + 60 = 0

(4 + 5, 0), (4 - 5, 0)

Solution steps

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

Calculate Hyperbola properties

4 x^{2} - y^{2} - 32 x + 60 = 0 :

Right-left Hyperbola with

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

(4 + c, 0), (4 - c, 0)

Compute

c :

c = 1^{2} + 2^{2} : 5

(4 + 5, 0), (4 - 5, 0)

\frac{x ^{2}}{625} - \frac{y ^{2}}{3600} = 1

5 x^{2} - 4 y^{2} - 40 x + 24 y + 24 = 0

\frac{y ^{2}}{25} - \frac{x ^{2}}{64} = 1

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

16 y^{2} + 64 y - x^{2} + 2 x = 1

What is the foci 4x^2-y^2-32x+60=0 ?
The foci 4x^2-y^2-32x+60=0 is (4+sqrt(5),0),(4-sqrt(5),0)