What is the foci x^2+6x=9y^2 ?

The foci x^2+6x=9y^2 is (-3+sqrt(10),0),(-3-sqrt(10),0)

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foci x^2+6x=9y^2

foci

x^{2} + 6 x = 9 y^{2}

(- 3 + 10, 0), (- 3 - 10, 0)

Solution steps

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

Calculate Hyperbola properties

x^{2} + 6 x = 9 y^{2} :

Right-left Hyperbola with

(h, k) = (- 3, 0), a = 3, b = 1

(- 3 + c, 0), (- 3 - c, 0)

Compute

c :

c = 3^{2} + 1^{2} : 10

(- 3 + 10, 0), (- 3 - 10, 0)

\frac{x ^{2}}{140} - \frac{( y - 6 ) ^{2}}{4} = 1

\frac{x ^{2}}{9} - \frac{y ^{2}}{36} = 1

\frac{x ^{2}}{4} - \frac{( y - 6 ) ^{2}}{140} = 1

\frac{y ^{2}}{5} - \frac{x ^{2}}{5} = 1

(x - 3)^{2} - \frac{y ^{2}}{9} = 1

What is the foci x^2+6x=9y^2 ?
The foci x^2+6x=9y^2 is (-3+sqrt(10),0),(-3-sqrt(10),0)