What is the foci 4x^2-y^2-24x-4y+28=0 ?

The foci 4x^2-y^2-24x-4y+28=0 is (3+sqrt(5),-2),(3-sqrt(5),-2)

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foci 4x^2-y^2-24x-4y+28=0

foci

4 x^{2} - y^{2} - 24 x - 4 y + 28 = 0

(3 + 5, - 2), (3 - 5, - 2)

Solution steps

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

Calculate Hyperbola properties

4 x^{2} - y^{2} - 24 x - 4 y + 28 = 0 :

Right-left Hyperbola with

(h, k) = (3, - 2), a = 1, b = 2

(3 + c, - 2), (3 - c, - 2)

Compute

c :

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

(3 + 5, - 2), (3 - 5, - 2)

\frac{x ^{2}}{64} - \frac{y ^{2}}{36} = 1

7 x^{2} - 9 y^{2} - 14 x + 72 y - 200 = 0

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

\frac{x ^{2}}{25} - \frac{y ^{2}}{49} = 1

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

What is the foci 4x^2-y^2-24x-4y+28=0 ?
The foci 4x^2-y^2-24x-4y+28=0 is (3+sqrt(5),-2),(3-sqrt(5),-2)