What is the foci 9x^2-4y^2-54x-16y+29=0 ?

The foci 9x^2-4y^2-54x-16y+29=0 is (3+sqrt(13),-2),(3-sqrt(13),-2)

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foci 9x^2-4y^2-54x-16y+29=0

foci

9 x^{2} - 4 y^{2} - 54 x - 16 y + 29 = 0

(3 + 13, - 2), (3 - 13, - 2)

Solution steps

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

Calculate Hyperbola properties

9 x^{2} - 4 y^{2} - 54 x - 16 y + 29 = 0 :

Right-left Hyperbola with

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

(3 + c, - 2), (3 - c, - 2)

Compute

c :

c = 2^{2} + 3^{2} : 13

(3 + 13, - 2), (3 - 13, - 2)

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

\frac{y ^{2}}{16} - \frac{x ^{2}}{1} = 1

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

\frac{( x ) ^{2}}{\frac{25}{4}} - \frac{( y ) ^{2}}{\frac{11}{4}} = 1

\frac{x ^{2}}{4} - \frac{3 y ^{2}}{4} = 1

What is the foci 9x^2-4y^2-54x-16y+29=0 ?
The foci 9x^2-4y^2-54x-16y+29=0 is (3+sqrt(13),-2),(3-sqrt(13),-2)