What is the foci-x^2+8x+4y^2-40y+88=0 ?

The foci-x^2+8x+4y^2-40y+88=0 is (4+sqrt(5),5),(4-sqrt(5),5)

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foci-x^2+8x+4y^2-40y+88=0

foci

- x^{2} + 8 x + 4 y^{2} - 40 y + 88 = 0

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

Solution steps

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

Calculate Hyperbola properties

- x^{2} + 8 x + 4 y^{2} - 40 y + 88 = 0 :

Right-left Hyperbola with

(h, k) = (4, 5), a = 2, b = 1

(4 + c, 5), (4 - c, 5)

Compute

c :

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

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

\frac{( y + 2 ) ^{2}}{36} - x^{2} = 1

\frac{x ^{2}}{23} - \frac{y ^{2}}{2} = 1

9 x^{2} - 16 y^{2} - 18 x + 64 y - 199 = 0

49 y^{2} - 100 x^{2} = 4900

\frac{x ^{2}}{64} - \frac{y ^{2}}{4} = 1

What is the foci-x^2+8x+4y^2-40y+88=0 ?
The foci-x^2+8x+4y^2-40y+88=0 is (4+sqrt(5),5),(4-sqrt(5),5)