What is the foci 4x^2-9y^2+32x-18y+37=0 ?

The foci 4x^2-9y^2+32x-18y+37=0 is (-4+sqrt(13/2),-1),(-4-sqrt(13/2),-1)

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foci 4x^2-9y^2+32x-18y+37=0

foci

4 x^{2} - 9 y^{2} + 32 x - 18 y + 37 = 0

(- 4 + \frac{13}{2}, - 1), (- 4 - \frac{13}{2}, - 1)

Solution steps

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

Calculate Hyperbola properties

4 x^{2} - 9 y^{2} + 32 x - 18 y + 37 = 0 :

Right-left Hyperbola with

(h, k) = (- 4, - 1), a = \frac{3}{2}, b = 2

(- 4 + c, - 1), (- 4 - c, - 1)

Compute

c :

c = (\frac{3}{2})^{2} + 2^{2} : \frac{13}{2}

(- 4 + \frac{13}{2}, - 1), (- 4 - \frac{13}{2}, - 1)

- 4 x^{2} + y^{2} + 40 x - 136 = 0

\frac{y ^{2}}{225} - \frac{x ^{2}}{324} = 1

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

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

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

What is the foci 4x^2-9y^2+32x-18y+37=0 ?
The foci 4x^2-9y^2+32x-18y+37=0 is (-4+sqrt(13/2),-1),(-4-sqrt(13/2),-1)