What is the foci 4x^2-y^2-24x+20=0 ?

The foci 4x^2-y^2-24x+20=0 is (3+2sqrt(5),0),(3-2sqrt(5),0)

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foci 4x^2-y^2-24x+20=0

foci

4 x^{2} - y^{2} - 24 x + 20 = 0

(3 + 25, 0), (3 - 25, 0)

Solution steps

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

Calculate Hyperbola properties

4 x^{2} - y^{2} - 24 x + 20 = 0 :

Right-left Hyperbola with

(h, k) = (3, 0), a = 2, b = 4

(3 + c, 0), (3 - c, 0)

Compute

c :

c = 2^{2} + 4^{2} : 25

(3 + 25, 0), (3 - 25, 0)

\frac{( x + 3 ) ^{2}}{9} - \frac{( y - 2 ) ^{2}}{16} = 1

9 x^{2} - y^{2} - 54 x - 2 y - 1 = 0

\frac{x ^{2}}{60} - \frac{y ^{2}}{40} = 1

\frac{( y + 2 ) ^{2}}{9} - \frac{( x - 1 ) ^{2}}{64} = 1

\frac{x ^{2}}{37} - \frac{y ^{2}}{63} = 1

What is the foci 4x^2-y^2-24x+20=0 ?
The foci 4x^2-y^2-24x+20=0 is (3+2sqrt(5),0),(3-2sqrt(5),0)