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

The vertices-4y^2+9x^2-27x-16y=2 is (7/3 ,-2),(2/3 ,-2)

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

vertices

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

(\frac{7}{3}, - 2), (\frac{2}{3}, - 2)

Solution steps

(h + a, k), (h - a, 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} + \frac{5}{6}, - 2), (\frac{3}{2} - \frac{5}{6}, - 2)

Refine

(\frac{7}{3}, - 2), (\frac{2}{3}, - 2)

\frac{( y + 3 ) ^{2}}{4} - \frac{( x + 1 ) ^{2}}{49} = 1

\frac{( x - 3 ) ^{2}}{16} - \frac{( y - 2 ) ^{2}}{25} = 1

\frac{x ^{2}}{144} - \frac{y ^{2}}{81} = 1

9 y^{2} - 16 x^{2} = 144

\frac{x ^{2}}{a ^{2}} - \frac{y ^{2}}{b ^{2}} = 1

What is the vertices-4y^2+9x^2-27x-16y=2 ?
The vertices-4y^2+9x^2-27x-16y=2 is (7/3 ,-2),(2/3 ,-2)