What is the foci x^2-y^2-4x+4y+9=0 ?

The foci x^2-y^2-4x+4y+9=0 is (2,2+3sqrt(2)),(2,2-3sqrt(2))

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foci x^2-y^2-4x+4y+9=0

foci

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

(2, 2 + 32), (2, 2 - 32)

Solution steps

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

Calculate Hyperbola properties

x^{2} - y^{2} - 4 x + 4 y + 9 = 0 :

Up-down Hyperbola with

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

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

Compute

c :

c = 3^{2} + 3^{2} : 32

(2, 2 + 32), (2, 2 - 32)

\frac{( x + 3 ) ^{2}}{25} - \frac{( y - 2 ) ^{2}}{49} = 1

4 y^{2} - x^{2} = 900

- \frac{( x - 2 ) ^{2}}{5} + \frac{( y + 1 ) ^{2}}{9} = 1

\frac{x ^{2}}{64} - \frac{y ^{2}}{32} = 1

25 y^{2} - 81 x^{2} = 2025

What is the foci x^2-y^2-4x+4y+9=0 ?
The foci x^2-y^2-4x+4y+9=0 is (2,2+3sqrt(2)),(2,2-3sqrt(2))