What is the foci 4x^2-4y^2+20x-16y+25=0 ?

The foci 4x^2-4y^2+20x-16y+25=0 is (-5/2 ,-2+2sqrt(2)),(-5/2 ,-2-2sqrt(2))

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foci 4x^2-4y^2+20x-16y+25=0

foci

4 x^{2} - 4 y^{2} + 20 x - 16 y + 25 = 0

(- \frac{5}{2}, - 2 + 22), (- \frac{5}{2}, - 2 - 22)

Solution steps

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

Calculate Hyperbola properties

4 x^{2} - 4 y^{2} + 20 x - 16 y + 25 = 0 :

Up-down Hyperbola with

(h, k) = (- \frac{5}{2}, - 2), a = 2, b = 2

(- \frac{5}{2}, - 2 + c), (- \frac{5}{2}, - 2 - c)

Compute

c :

c = 2^{2} + 2^{2} : 22

(- \frac{5}{2}, - 2 + 22), (- \frac{5}{2}, - 2 - 22)

\frac{x ^{2}}{25} - \frac{y ^{2}}{81} = 1

3 x^{2} - 4 y^{2} = 12

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

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

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

What is the foci 4x^2-4y^2+20x-16y+25=0 ?
The foci 4x^2-4y^2+20x-16y+25=0 is (-5/2 ,-2+2sqrt(2)),(-5/2 ,-2-2sqrt(2))