What is the vertices 9x^2-4y^2+54x-8y+78=0 ?

The vertices 9x^2-4y^2+54x-8y+78=0 is (-3,-1/2),(-3,-3/2)

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vertices 9x^2-4y^2+54x-8y+78=0

vertices

9 x^{2} - 4 y^{2} + 54 x - 8 y + 78 = 0

(- 3, - \frac{1}{2}), (- 3, - \frac{3}{2})

Solution steps

(h, k + a), (h, k - a)

Calculate Hyperbola properties

9 x^{2} - 4 y^{2} + 54 x - 8 y + 78 = 0 :

Up-down Hyperbola with

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

(- 3, - 1 + \frac{1}{2}), (- 3, - 1 - \frac{1}{2})

Refine

(- 3, - \frac{1}{2}), (- 3, - \frac{3}{2})

x^{2} - y^{2} < 1

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

4 y^{2} - x^{2} + 40 y - 4 x + 60 = 0

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

\frac{( x - 3 ) ^{2}}{9} - \frac{( y + 4 ) ^{2}}{25} = 1

What is the vertices 9x^2-4y^2+54x-8y+78=0 ?
The vertices 9x^2-4y^2+54x-8y+78=0 is (-3,-1/2),(-3,-3/2)