What is the foci-4y^2+9x^2-27x-16y=2 ?

The foci-4y^2+9x^2-27x-16y=2 is ((18+5sqrt(13))/(12),-2),((18-5sqrt(13))/(12),-2)

Popular >

foci-4y^2+9x^2-27x-16y=2

foci

- 4 y^{2} + 9 x^{2} - 27 x - 16 y = 2

(\frac{18 + 5 13}{12}, - 2), (\frac{18 - 5 13}{12}, - 2)

Solution steps

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

Calculate Hyperbola properties

- 4 y^{2} + 9 x^{2} - 27 x - 16 y = 2 :

Right-left Hyperbola with

(h, k) = (\frac{3}{2}, - 2), a = \frac{5}{6}, b = \frac{5}{4}

(\frac{3}{2} + c, - 2), (\frac{3}{2} - c, - 2)

Compute

c :

c = (\frac{5}{6})^{2} + (\frac{5}{4})^{2} : \frac{5 13}{12}

(\frac{3}{2} + \frac{5 13}{12}, - 2), (\frac{3}{2} - \frac{5 13}{12}, - 2)

Refine

(\frac{18 + 5 13}{12}, - 2), (\frac{18 - 5 13}{12}, - 2)

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

- 9 x^{2} + 4 y^{2} = 36

- 4 x^{2} + y^{2} = 16

- \frac{x ^{2}}{16} + \frac{y ^{2}}{36} = 1

\frac{y ^{2}}{25} - \frac{( x - 2 ) ^{2}}{0} = 1

What is the foci-4y^2+9x^2-27x-16y=2 ?
The foci-4y^2+9x^2-27x-16y=2 is ((18+5sqrt(13))/(12),-2),((18-5sqrt(13))/(12),-2)