What is -9x^2+y^2+54x-117=0 ?

The solution to -9x^2+y^2+54x-117=0 is Hyperbola with (h,k)=(3,0),a=6,b=2

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-9x^2+y^2+54x-117=0

- 9 x^{2} + y^{2} + 54 x - 117 = 0

(h, k) = (3, 0), a = 6, b = 2

Solution steps

- 9 x^{2} + y^{2} + 54 x - 117 = 0

Rewrite

- 9 x^{2} + y^{2} + 54 x - 117 = 0

in the form of a standard hyperbola equation

\frac{( y - 0 ) ^{2}}{6 ^{2}} - \frac{( x - 3 ) ^{2}}{2 ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (3, 0), a = 6, b = 2

y^{2} = 6^{2} + x^{2} + 2 \cdot 6 \cdot x \cdot 0.5

y^{1} y = (x + 2) (x - 1)

3 (x - 1)^{2} = 6 + 2 (y + 1)^{2}

(x - 5)^{2} - (y - 4)^{2} = 25

x^{2} - 3 y^{2} = 4

What is -9x^2+y^2+54x-117=0 ?
The solution to -9x^2+y^2+54x-117=0 is Hyperbola with (h,k)=(3,0),a=6,b=2