What is the vertices 4x^2-24x-36y^2-360y+864=0 ?

The vertices 4x^2-24x-36y^2-360y+864=0 is (3,-5+4sqrt(3)),(3,-5-4sqrt(3))

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vertices 4x^2-24x-36y^2-360y+864=0

vertices

4 x^{2} - 24 x - 36 y^{2} - 360 y + 864 = 0

(3, - 5 + 43), (3, - 5 - 43)

Solution steps

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

Calculate Hyperbola properties

4 x^{2} - 24 x - 36 y^{2} - 360 y + 864 = 0 :

Up-down Hyperbola with

(h, k) = (3, - 5), a = 43, b = 123

(3, - 5 + 43), (3, - 5 - 43)

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

\frac{( y - 6 ) ^{2}}{36} - \frac{( x + 1 ) ^{2}}{16} = 1

x^{2} - 4 y^{2} - 2 x + 16 y = 20

\frac{( y - 1 ) ^{2}}{16} - \frac{( x + 6 ) ^{2}}{81} = 1

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

What is the vertices 4x^2-24x-36y^2-360y+864=0 ?
The vertices 4x^2-24x-36y^2-360y+864=0 is (3,-5+4sqrt(3)),(3,-5-4sqrt(3))